{"id":153892,"date":"2022-03-25T22:55:44","date_gmt":"2022-03-25T17:25:44","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/equivalent-sets-significance-examples-solved-examples-and-faqs\/"},"modified":"2022-12-31T17:22:00","modified_gmt":"2022-12-31T11:52:00","slug":"equivalent-sets-significance-examples-solved-examples-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/","title":{"rendered":"Equivalent Sets &#8211; Significance, Examples, Solved Examples, and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">Table of 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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Equivalent_Set_and_its_Significance\" title=\"Equivalent Set and its Significance\">Equivalent Set and its Significance<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Equivalent_Set_Definition\" title=\"Equivalent Set Definition\">Equivalent Set Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Equal_Set\" title=\"Equal Set\">Equal Set<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Equal_Set_Example\" title=\"Equal Set Example\">Equal Set Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Symbol_of_Equal_Set\" title=\"Symbol of Equal Set\">Symbol of Equal Set<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Equivalent_Set_Example\" title=\"Equivalent Set Example\">Equivalent Set Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Equivalent_Sets_Symbol\" title=\"Equivalent Sets Symbol\">Equivalent Sets Symbol<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#Relation_Between_Equal_and_Equivalent_Sets\" title=\"Relation Between Equal and Equivalent Sets\">Relation Between Equal and Equivalent Sets<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/equivalent-sets\/#i\" title=\":\">:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Equivalent_Set_and_its_Significance\"><\/span>Equivalent Set and its Significance<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Equivalent set is a set that has the same cardinality as another set. In other words, the two sets have the same number of elements. The significance of equivalent sets is that they can be used to represent other sets. For example, if you are given a set of numbers, you can represent it using an equivalent set. This can be helpful when you are trying to solve a problem or when you are trying to understand a concept.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153891 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/equivalent-sets-significance-examples-solved-examples-and-faqs.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/equivalent-sets-significance-examples-solved-examples-and-faqs.jpg?v=1648229139 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/equivalent-sets-significance-examples-solved-examples-and-faqs-300x212.jpg?v=1648229139 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equivalent_Set_Definition\"><\/span>Equivalent Set Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An equivalence relation is a binary relation that is reflexive, symmetric, and transitive.<\/p>\n<p>Reflexive : For all a in A, aRb if and only if a=b.<\/p>\n<p>: For all a in A, aRb if and only if a=b. Symmetric : For all a,b in A, aRb if and only if bRa.<\/p>\n<p>: For all a,b in A, aRb if and only if bRa. Transitive: For all a,b,c in A, aRb and bRc if and only if a=c.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equal_Set\"><\/span>Equal Set<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If we take two sets, A and B, and consider them to be equal, then this means that every element in A is also an element in B, and vice versa. In other words, the sets are identical. Symbolically, we can write this as:<\/p>\n<p>A = B<\/p>\n<p>This equality can be tested mathematically, by checking to see if the two sets have the same size (that is, if they have the same number of elements).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equal_Set_Example\"><\/span>Equal Set Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>We can use the equal set operator to create a set of all the integers that are equal to 7.<\/p>\n<p>The set {7} is created.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Symbol_of_Equal_Set\"><\/span>Symbol of Equal Set<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The symbol of an equal set is two parallel lines.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equivalent_Set_Example\"><\/span>Equivalent Set Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>{1, 2, 3}<\/p>\n<p>The equivalent set is {1, 2, 3, 4, 5}.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equivalent_Sets_Symbol\"><\/span>Equivalent Sets Symbol<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A set of all real numbers<\/p>\n<p>A set of all natural numbers<\/p>\n<p>A set of all rational numbers<\/p>\n<p>A set of all irrational numbers<\/p>\n<p>A set of all positive real numbers<\/p>\n<p>A set of all negative real numbers<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Relation_Between_Equal_and_Equivalent_Sets\"><\/span>Relation Between Equal and Equivalent Sets<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A set is equal to another set if and only if the two sets have the same elements. A set is equivalent to another set if and only if the two sets have the same cardinality.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"i\"><\/span>:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>I was very pleased with the quality of the product and the ease of the installation.<\/p>\n<p>5 out of 5 stars Comfort<\/p>\n<p>5 out of 5 stars Quality<\/p>\n<p>5 out of 5 stars Value<\/p>\n<p>5 out of 5 stars Installation<\/p>\n<p>5 out of 5 stars Reliability<\/p>\n<p>Purchased on Dec 21, 2016<\/p>\n<p>Reviewed on Feb 8, 2017<\/p>\n<p>I was very pleased with the quality of the product and the ease of the installation.<\/p>\n<p>5 out of 5 stars Comfort<\/p>\n<p>5 out of 5 stars Quality<\/p>\n<p>5 out of 5 stars Value<\/p>\n<p>5 out of 5 stars Installation<\/p>\n<p>5 out of 5 stars Reliability<\/p>\n<p>Purchased on Dec 21, 2016<\/p>\n<p>Reviewed on Feb 8, 2017<\/p>\n<p>I was very pleased with the quality of the product and the ease of the installation.<\/p>\n<p>5 out of 5 stars Comfort<\/p>\n<p>5 out of 5 stars Quality<\/p>\n<p>5 out of 5 stars Value<\/p>\n<p>5 out of 5 stars Installation<\/p>\n<p>5 out of 5 stars Reliability<\/p>\n<p>Purchased on Dec 21, 2016<\/p>\n<p>Reviewed on Feb 8, 2017<\/p>\n<p>I was very pleased with the quality of the product and the ease of the installation.<\/p>\n<p>5 out of 5 stars Comfort<\/p>\n<p>5 out of 5 stars Quality<\/p>\n<p>5 out of 5 stars Value<\/p>\n<p>5 out of 5 stars Installation<\/p>\n<p>5 out of 5 stars Reliability<\/p>\n<p>Purchased on<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Equivalent Set and its Significance Equivalent set is a set that has the same cardinality as another set. In other [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Equivalent Sets","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Learn about equivalent sets topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.","custom_permalink":"maths\/equivalent-sets\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equivalent Sets - Significance, Examples, Solved Examples, and FAQs<\/title>\n<meta name=\"description\" content=\"Learn about equivalent sets topic of maths in details explained by subject experts on infinitylearn.com. 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