{"id":19959,"date":"2024-02-01T21:06:12","date_gmt":"2024-02-01T20:06:12","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=19959"},"modified":"2024-02-11T21:29:21","modified_gmt":"2024-02-11T20:29:21","slug":"ex-algebre-relationnelle","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/","title":{"rendered":"11 Corrected Exercises Relational Algebra"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"19959\" class=\"elementor elementor-19959\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b8a0092 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b8a0092\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9149fde\" data-id=\"9149fde\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fb82597 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"fb82597\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Software 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class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-77dca8b\" data-id=\"77dca8b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c179dec elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c179dec\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/UML_(informatique)\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5887ac4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5887ac4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-50b27ca\" data-id=\"50b27ca\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-489f897 elementor-widget elementor-widget-heading\" data-id=\"489f897\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercices-corriges-Algebre-Relationnelle\" >Corrected exercises Relational Algebra<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-1\" >Exercise 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-2\" >Exercise 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-3\" >Exercise 3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-4\" >Exercise 4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-5\" >Exercise 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-6\" >Exercise 6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-7\" >Exercise 7<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-8\" >Exercise 8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-9\" >Exercise 9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-10\" >Exercise 10<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/complex-systems-ai.com\/en\/software-analysis\/corrected-exercises-relational-algebra\/#Exercice-11\" >Exercise 11<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-corriges-Algebre-Relationnelle\"><\/span>Corrected exercises Relational Algebra<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cf9c367 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cf9c367\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-65d6022\" data-id=\"65d6022\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-73b1d92 elementor-widget elementor-widget-text-editor\" data-id=\"73b1d92\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This page contains exercises corrected in <a href=\"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/\">Algebra<\/a> Relational.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"Relational Algebra\" width=\"97\" height=\"97\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-624f4ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"624f4ca\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-523cd73\" data-id=\"523cd73\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0de4e1f elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"0de4e1f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f58850b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f58850b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bcd9f7d\" data-id=\"bcd9f7d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b1dceaf elementor-widget elementor-widget-heading\" data-id=\"b1dceaf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-1\"><\/span>Exercise 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-003e9f3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"003e9f3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-be24212\" data-id=\"be24212\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a1a47e3 elementor-widget elementor-widget-text-editor\" data-id=\"a1a47e3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>We will study relational algebra through an example database and a set of queries expressed on this database. The database considered is described by the following diagram:<\/p><p>PLAYER (Last name, First name, Age, Nationality)<\/p><p>MEETING (Winner Name, Loser Name, Tournament Location, Year, Score)<\/p><p>WIN(PlayerName, Tournament Location, Year, Rank, Bonus, Sponsor Name)<\/p><p>SPONSOR (Name,Tournament Location,Year,Address,MtContribution)<\/p><p>The PLAYER relationship contains all licensed players.<\/p><p>The MEETING relationship describes for each tournament, the set \u03c0 of meetings between two players (a winner and a loser). The relationship also describes the score achieved at each meeting. The following assumptions are made about tournaments:<\/p><ul><li>two players only meet once in a tournament,<\/li><li>a player can win against several other players in a tournament,<\/li><li>a player can lose several times in a tournament,<\/li><li>a player participates in one or more tournaments.<\/li><\/ul><p>The GAIN relationship contains the bonuses and sponsorships of players who have already participated in a tournament. Whatever the result of a player, he receives a single bonus per tournament (so he only has one gain per tournament), the amount of which is correlated to the rank he occupies in this tournament.<\/p><p>The SPONSOR relationship contains the references of the sponsors and the amount of their contribution to each tournament.<\/p><p><span style=\"color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-size: 1.125rem; font-weight: var( --e-global-typography-text-font-weight );\">Express the following queries on this database using relational algebra. Give the functional expressions and corresponding algebraic trees (i.e. graphs of relational operators).<\/span><\/p><p><em>R1: Name and bonuses of players sponsored by Peugeot between 1985 and 1990.<\/em><\/p><p><em>R2: Name and age of players who participated in the 1989 Roland Garros tournament. <\/em><\/p><p><em>R3: Name and nationality of players sponsored by Peugeot and having won at least one match at Roland Garros.<\/em><\/p><p><em>R4: Name and nationality of players who participated in both the Roland Garros tournament and the Wimbledon tournament in 1985.<\/em><\/p><p><em>R5: Name of players having all their bonuses from Roland Garros tournaments greater than 1MF.<\/em><\/p><p><em>R6: Name, first name, age and nationality of players who participated in all Roland Garros.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1ee8107 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1ee8107\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f98824c\" data-id=\"f98824c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b9bd501 elementor-widget elementor-widget-toggle\" data-id=\"b9bd501\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1941\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1941\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1941\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1941\"><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-20010 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd31-1.png\" alt=\"relational algebra\" width=\"512\" height=\"578\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd31-1.png 512w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd31-1-266x300.png 266w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd31-1-11x12.png 11w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p><p><img decoding=\"async\" class=\"alignnone wp-image-20011 size-medium\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd32-300x196.png\" alt=\"relational algebra\" width=\"300\" height=\"196\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd32-300x196.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd32-18x12.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd32.png 601w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20012 size-medium\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd33-300x249.png\" alt=\"relational algebra\" width=\"300\" height=\"249\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd33-300x249.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd33-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd33.png 588w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20013 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd34.png\" alt=\"relational algebra\" width=\"642\" height=\"403\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd34.png 642w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd34-300x188.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd34-18x12.png 18w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20014 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd35.png\" alt=\"relational algebra\" width=\"628\" height=\"468\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd35.png 628w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd35-300x224.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd35-16x12.png 16w\" sizes=\"(max-width: 628px) 100vw, 628px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20015 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd36.png\" alt=\"relational algebra\" width=\"630\" height=\"164\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd36.png 630w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd36-300x78.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd36-18x5.png 18w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-51a1a61 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"51a1a61\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-00a6f96\" data-id=\"00a6f96\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-46ebf7a elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"46ebf7a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-86a335d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"86a335d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dbe4bae\" data-id=\"dbe4bae\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0522cf7 elementor-widget elementor-widget-heading\" data-id=\"0522cf7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-2\"><\/span>Exercise 2<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-906df74 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"906df74\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e1ddc08\" data-id=\"e1ddc08\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0d3a1b1 elementor-widget elementor-widget-text-editor\" data-id=\"0d3a1b1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Translate, using one or two sentences into French, the meaning of the following algebraic questions:<\/p><p>a) Join(Join(Div(MEETING{WinnerName,LoserName,TournamentPlace,Year}, MEETING{TournamentPlace,Year}),<span style=\"font-size: 1.125rem;\">\u00a0 \u00a0 PLAYER \/ WinnerName = Name),<\/span><span style=\"font-size: 1.125rem;\">\u00a0 PLAYER \/ LoserName = LastName){WinnerName,FirstName,LoserLastName,FirstName}<\/span><\/p><p>b) Diff<strong>(<\/strong>Join<strong>(<\/strong>MEETING{LoseName}, PLAYER{Last Name, First Name} \/ Last Name = LoserName<strong style=\"font-size: 1.125rem;\">), <\/strong><span style=\"font-size: 1.125rem;\">\u00a0Join<\/span><strong style=\"font-size: 1.125rem;\">(<\/strong><span style=\"font-size: 1.125rem;\">MEETING {NameWinner},<\/span><span style=\"font-size: 1.125rem;\">\u00a0 \u00a0 \u00a0PLAYER{Last Name, First Name} \/ Last Name = WinnerName<\/span><strong style=\"font-size: 1.125rem;\">)<\/strong><strong style=\"font-size: 1.125rem;\">).<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e826cd3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e826cd3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-90005a0\" data-id=\"90005a0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-85b4286 elementor-widget elementor-widget-toggle\" data-id=\"85b4286\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1401\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1401\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1401\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1401\"><p>In French, the proposed algebraic queries are paraphrased as follows:<\/p><p><strong><em>To)<\/em><\/strong><em> Name and first name of the pairs of players meeting each other at all tournaments and the first of whom has always won against the second.<\/em><\/p><p><strong><em>b) <\/em><\/strong><em>Name and first name of players who have always lost.<\/em><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-395bbac elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"395bbac\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c2ac5f0\" data-id=\"c2ac5f0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6f6bb83 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"6f6bb83\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ec8e269 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ec8e269\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dc4237f\" data-id=\"dc4237f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4710e57 elementor-widget elementor-widget-heading\" data-id=\"4710e57\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-3\"><\/span>Exercise 3<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e23a56f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e23a56f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f5d9199\" data-id=\"f5d9199\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3926e80 elementor-widget elementor-widget-text-editor\" data-id=\"3926e80\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Give the algebraic expression for the division.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d557320 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d557320\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-696974a\" data-id=\"696974a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b767451 elementor-widget elementor-widget-toggle\" data-id=\"b767451\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1921\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1921\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1921\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1921\"><p>R(X,Y) \/ S(Y) = pi<sub>X<\/sub> (R) \u2013 pi<sub>X<\/sub> ((S x pi<sub>X<\/sub> (R) \u2013 R).<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a49949f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a49949f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1b44e71\" data-id=\"1b44e71\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e0b1797 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"e0b1797\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c7b1a6d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c7b1a6d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-26bbb35\" data-id=\"26bbb35\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b2ce242 elementor-widget elementor-widget-heading\" data-id=\"b2ce242\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-4\"><\/span>Exercise 4<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a6b84ae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a6b84ae\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b54e06e\" data-id=\"b54e06e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6602f41 elementor-widget elementor-widget-text-editor\" data-id=\"6602f41\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Consider the following base:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19975 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd11.png\" alt=\"relational algebra\" width=\"540\" height=\"146\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd11.png 540w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd11-300x81.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd11-18x5.png 18w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p><p>What are the following expressions:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19976 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd12.png\" alt=\"relational algebra\" width=\"510\" height=\"94\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd12.png 510w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd12-300x55.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd12-18x3.png 18w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-05c7aa1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"05c7aa1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6b38af2\" data-id=\"6b38af2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c443243 elementor-widget elementor-widget-toggle\" data-id=\"c443243\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2051\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2051\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2051\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2051\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19977 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd13.png\" alt=\"relational algebra\" width=\"509\" height=\"348\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd13.png 509w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd13-300x205.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd13-18x12.png 18w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7eecd9b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7eecd9b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f93a9ea\" data-id=\"f93a9ea\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2877dd3 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"2877dd3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8bbe2fb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8bbe2fb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-86c32ee\" data-id=\"86c32ee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1d2c29a elementor-widget elementor-widget-heading\" data-id=\"1d2c29a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-5\"><\/span>Exercise 5<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2a40ed1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a40ed1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f520fac\" data-id=\"f520fac\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-35b7ba9 elementor-widget elementor-widget-text-editor\" data-id=\"35b7ba9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Exercise 3 We consider the following relationships:<\/p><p>PERSON (CIN, NAME, First name, Address)<\/p><p>Car (Grey Card, CIN, Model)<\/p><p>Motorcycle (NCarteGrise, CIN, Model)<\/p><p>Write the expressions representing:<\/p><p>1. Show people who own a car but not a motorcycle?<\/p><p>2. Show people who own a car and a motorcycle?<\/p><p>3. Show people who don&#039;t own a car or motorcycle?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9cd6832 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9cd6832\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4c32b5d\" data-id=\"4c32b5d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8e76bf5 elementor-widget elementor-widget-toggle\" data-id=\"8e76bf5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1491\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1491\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1491\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1491\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19978 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd14.png\" alt=\"relational algebra\" width=\"679\" height=\"242\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd14.png 679w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd14-300x107.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd14-18x6.png 18w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5dacde8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5dacde8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-88b8016\" data-id=\"88b8016\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4843bd2 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"4843bd2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ca97ed7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ca97ed7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-817e7ce\" data-id=\"817e7ce\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cd4364f elementor-widget elementor-widget-heading\" data-id=\"cd4364f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-6\"><\/span>Exercise 6<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bc15557 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bc15557\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-997851d\" data-id=\"997851d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bae22bb elementor-widget elementor-widget-text-editor\" data-id=\"bae22bb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Consider the schema of the following Library database:<\/p><p>Student(NumEtd,LastNameEtd,FirstNameEdt,AddressAndd) <br \/>Book(BookNum,BookTitle,AuthorNum,PublisherNum,ThemeNum,EditionYear) <br \/>Author(AuthorNum,AuthorName,AuthorAddress) <br \/>Publisher(EditorNum,EditorName,EditorAddress) <br \/>Theme(ThemeNum,ThemeTitle) <br \/>Ready(EtdNum,BookNum,ReadyDate,ReturnDate)<\/p><p>Primary keys in bold and foreign keys in italics.<\/p><p>Write the following queries in algebraic language:<\/p><p>1. The name, first name and address of the student named &#039;Alami&#039;<\/p><p>2. The author number &#039;Alami&#039;<\/p><p>3. the list of books by the author number 121<\/p><p>4. books by author name &#039;Alami&#039;<\/p><p>5. the number of the author of the book &#039;how to get 20 in BDD&#039;<\/p><p>6. the name and address of the author of the book &#039;how to get 20 in BDD&#039;<\/p><p>7. Books by the author &#039;Alami&#039; published by the publisher &#039;Nul part&#039;<\/p><p>8. books by the author &#039;Alami&#039; or &#039;Belhadj&#039;<\/p><p>9. books that have never been borrowed<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4cdd7e0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4cdd7e0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-862a607\" data-id=\"862a607\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-00f74e5 elementor-widget elementor-widget-toggle\" data-id=\"00f74e5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1011\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1011\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1011\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1011\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19980 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15.png\" alt=\"relational algebra\" width=\"503\" height=\"225\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15.png 503w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15-300x134.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15-18x8.png 18w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19981 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16.png\" alt=\"relational algebra\" width=\"664\" height=\"501\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16.png 664w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16-300x226.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16-16x12.png 16w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1415958 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1415958\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9efb7ab\" data-id=\"9efb7ab\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6d9b3a8 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"6d9b3a8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0111bd3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0111bd3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-efc7a63\" data-id=\"efc7a63\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2e424f1 elementor-widget elementor-widget-heading\" data-id=\"2e424f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-7\"><\/span>Exercise 7<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-110ace6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"110ace6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-84bb053\" data-id=\"84bb053\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4d41e53 elementor-widget elementor-widget-text-editor\" data-id=\"4d41e53\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the rest of the tutorial, we will consider the following relationship diagrams with their intuitive meanings:<\/p><p>CJH (CourseId, Day, Time) The course whose identifier appears in the first component of a tuple takes place on the day specified in the second component, at the time which appears in the third component.<\/p><p>CS (IdCours, IdSalle) The course of the first component takes place in the room indicated in the second component.<\/p><p>ENA (EtudiantId, Name, Address) Students whose identifier appears as the first component of a tuple have a name and an address which appear respectively in the second and third component.<\/p><p>CEN (IdCours, IdEtudiant, Note) The student in the second component obtained the grade specified in the third component in the course specified in the first component.<\/p><p>These four diagrams form the database diagram which will be used for the exercises. An example of a possible current value for the database is shown below.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19982 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17.png\" alt=\"relational algebra\" width=\"710\" height=\"307\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17.png 710w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17-300x130.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17-18x8.png 18w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19987 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15-1.png\" alt=\"relational algebra\" width=\"584\" height=\"195\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15-1.png 584w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15-1-300x100.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd15-1-18x6.png 18w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19988 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16-1.png\" alt=\"relational algebra\" width=\"741\" height=\"154\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16-1.png 741w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16-1-300x62.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd16-1-18x4.png 18w\" sizes=\"(max-width: 741px) 100vw, 741px\" \/><\/p><p>1.7. Inspired by 1.5, show that division can be obtained from the difference, the Cartesian product and the projection.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-76f9438 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"76f9438\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-786a6ea\" data-id=\"786a6ea\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5d92a72 elementor-widget elementor-widget-toggle\" data-id=\"5d92a72\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9811\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-9811\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9811\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-9811\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19989 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17-1.png\" alt=\"relational algebra\" width=\"583\" height=\"665\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17-1.png 583w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17-1-263x300.png 263w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd17-1-11x12.png 11w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19990 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd18.png\" alt=\"relational algebra\" width=\"770\" height=\"636\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd18.png 770w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd18-300x248.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd18-768x634.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd18-15x12.png 15w\" sizes=\"(max-width: 770px) 100vw, 770px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ad2b87b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ad2b87b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-45a4523\" data-id=\"45a4523\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cdff1ff elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"cdff1ff\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e74598a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e74598a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-15d27f1\" data-id=\"15d27f1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4d9e8e6 elementor-widget elementor-widget-heading\" data-id=\"4d9e8e6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-8\"><\/span>Exercise 8<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5ef0d82 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5ef0d82\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-62bf0c7\" data-id=\"62bf0c7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9eeea99 elementor-widget elementor-widget-text-editor\" data-id=\"9eeea99\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Using the same tables as exercise 7, express the queries below in algebraic language:<\/p><p>2.1. Give the names of the students taking the &#039;Algo&#039; course.<\/p><p>2.2. Give the marks in &#039;Archi&#039; for the students whose name is &#039;Titi&#039;.<\/p><p>2.3. Give the pairs (day, time) for which room &#039;S1&#039; is occupied by a course.<\/p><p>2.4. Give the IDs of students who only have &#039;A&#039; grades<\/p><p>2.5. Give the room where &#039;Toto&#039; is on Monday at 9am.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-79894de elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"79894de\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4186c45\" data-id=\"4186c45\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-12cc5dc elementor-widget elementor-widget-toggle\" data-id=\"12cc5dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1971\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1971\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1971\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1971\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19991 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd19.png\" alt=\"relational algebra\" width=\"644\" height=\"693\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd19.png 644w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd19-279x300.png 279w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd19-11x12.png 11w\" sizes=\"(max-width: 644px) 100vw, 644px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-343d773 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"343d773\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2e4985a\" data-id=\"2e4985a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b8650b3 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"b8650b3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-db764a2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"db764a2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-17dbed7\" data-id=\"17dbed7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f739b60 elementor-widget elementor-widget-heading\" data-id=\"f739b60\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-9\"><\/span>Exercise 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3e1cf3d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3e1cf3d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ee9e11e\" data-id=\"ee9e11e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-15537f3 elementor-widget elementor-widget-text-editor\" data-id=\"15537f3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>On the same bases of exercise 7 and the queries of exercise 8.<\/p><p>3.1. Draw the expression tree for query 2.1, drag the restriction as low as you can.<\/p><p>3.2. Draw the expression tree for query 2.5, drag the restrictions and projections as low as you can.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2b3534d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b3534d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5697585\" data-id=\"5697585\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-363a63f elementor-widget elementor-widget-toggle\" data-id=\"363a63f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-5681\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-5681\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-5681\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-5681\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19992 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd20.png\" alt=\"relational algebra\" width=\"728\" height=\"394\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd20.png 728w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd20-300x162.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd20-18x10.png 18w\" sizes=\"(max-width: 728px) 100vw, 728px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19993 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd21.png\" alt=\"relational algebra\" width=\"759\" height=\"630\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd21.png 759w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd21-300x249.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd21-14x12.png 14w\" sizes=\"(max-width: 759px) 100vw, 759px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19994 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd22.png\" alt=\"relational algebra\" width=\"555\" height=\"649\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd22.png 555w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd22-257x300.png 257w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd22-10x12.png 10w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-00ae5fb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"00ae5fb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-54a50a2\" data-id=\"54a50a2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-80dc9f6 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"80dc9f6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0524e2c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0524e2c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-154765e\" data-id=\"154765e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4f91f52 elementor-widget elementor-widget-heading\" data-id=\"4f91f52\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-10\"><\/span>Exercise 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f74061c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f74061c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1f39c36\" data-id=\"1f39c36\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-836382d elementor-widget elementor-widget-text-editor\" data-id=\"836382d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Let R and S be the relations, where the attributes A, B, C are defined on the domains of the letters of the alphabet. Give the result of the following queries:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-19999 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd23.png\" alt=\"relational algebra\" width=\"398\" height=\"235\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd23.png 398w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd23-300x177.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd23-18x12.png 18w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p><p>Then check the following equations:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-20000\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd24.png\" alt=\"relational algebra\" width=\"168\" height=\"53\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd24.png 168w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd24-18x6.png 18w\" sizes=\"(max-width: 168px) 100vw, 168px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-acfe091 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"acfe091\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9a6d92c\" data-id=\"9a6d92c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db32a81 elementor-widget elementor-widget-toggle\" data-id=\"db32a81\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2291\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2291\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2291\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2291\"><p>The three queries are at the top, the 2 equations are wrong, the result is at the bottom.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20001 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd25.png\" alt=\"relational algebra\" width=\"374\" height=\"297\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd25.png 374w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd25-300x238.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd25-15x12.png 15w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4a12c16 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4a12c16\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-11416b6\" data-id=\"11416b6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0f8ba91 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"0f8ba91\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-eb2531c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"eb2531c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a8e1468\" data-id=\"a8e1468\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e25f73 elementor-widget elementor-widget-heading\" data-id=\"7e25f73\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-11\"><\/span>Exercise 11<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b3bb018 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b3bb018\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2ddd852\" data-id=\"2ddd852\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-78d605a elementor-widget elementor-widget-text-editor\" data-id=\"78d605a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Consider the two tables:<\/p><p>Employee Relations (EMP)\u00a0<\/p><p>EMP(ENO, ENOM, PROF, DATEEMB, SAL, COMM, DNO)\u00a0<\/p><p>ENO: employee number, key\u00a0<\/p><p>ENOM: employee name\u00a0<\/p><p>PROF: profession (director is not a profession)\u00a0<\/p><p>DATEEMB: date of hire\u00a0<\/p><p>SAL: salary\u00a0<\/p><p>COMM: commission (an employee may not have commission)\u00a0<\/p><p>DNO: department number to which the employee belongs\u00a0<\/p><p>Relations of Departments (DEPT)\u00a0<\/p><p>DEPT(DNO, DNOM, DIR, CITY)\u00a0<\/p><p>DNO: department number, key\u00a0<\/p><p>DNOM: name of department\u00a0<\/p><p>DIR: department director\u00a0<\/p><p>CITY: location of the department (city)<\/p><p>Express the following queries in relational algebra and then in SQL:<\/p><p>Query 1: Give all tuples of DEPT.<\/p><p>Query 2: Return all tuples of EMP.<\/p><p>Request 3: Give the names and salaries of employees.<\/p><p>Request 4: Give the employees&#039; professions (after elimination of duplicates).<\/p><p>Request 5: Give the hiring dates of the technicians.<\/p><p>Query 6: Make the Cartesian product between EMP and DEPT.<\/p><p>Query 7: Give the names of the employees and the names of their department.<\/p><p>Request 8: Give the numbers of employees working in BOSTON.<\/p><p>Request 9: Give the names of the directors of departments 1 and 3. Warning: director is not a profession!<\/p><p>Request 10: Give the names of employees working in a department with at least one engineer.<\/p><p>Request 11: Give the salary and name of employees earning more than one (at least one) engineer.<\/p><p>Request 12: Give the salary and name of employees earning more than all engineers.<\/p><p>Request 13: Give the names of employees and the names of their directors.<\/p><p>Query 14: Find the names of employees with the same manager as JIM. Please note: an employee can be director of several departments.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9e6bff7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9e6bff7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0eb60f7\" data-id=\"0eb60f7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f94cca3 elementor-widget elementor-widget-toggle\" data-id=\"f94cca3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2611\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2611\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2611\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2611\"><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20002 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd26.png\" alt=\"relational algebra\" width=\"582\" height=\"651\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd26.png 582w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd26-268x300.png 268w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd26-11x12.png 11w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20003 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd27.png\" alt=\"relational algebra\" width=\"709\" height=\"714\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd27.png 709w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd27-298x300.png 298w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd27-150x150.png 150w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd27-12x12.png 12w\" sizes=\"(max-width: 709px) 100vw, 709px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20004 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd28.png\" alt=\"relational algebra\" width=\"712\" height=\"283\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd28.png 712w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd28-300x119.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd28-18x7.png 18w\" sizes=\"(max-width: 712px) 100vw, 712px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20005 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd29.png\" alt=\"relational algebra\" width=\"698\" height=\"554\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd29.png 698w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd29-300x238.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd29-15x12.png 15w\" sizes=\"(max-width: 698px) 100vw, 698px\" \/><\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-20006 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd30.png\" alt=\"relational algebra\" width=\"709\" height=\"531\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd30.png 709w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd30-300x225.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2024\/02\/bdd30-16x12.png 16w\" sizes=\"(max-width: 709px) 100vw, 709px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Software analysis Wiki home page Corrected exercises in Relational Algebra This page contains corrected exercises in Relational Algebra. Statement We are going to study relational algebra in... <\/p>","protected":false},"author":1,"featured_media":0,"parent":4609,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-19959","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/19959","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=19959"}],"version-history":[{"count":25,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/19959\/revisions"}],"predecessor-version":[{"id":20488,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/19959\/revisions\/20488"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/4609"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=19959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}