{"id":156332,"date":"2022-03-26T01:38:22","date_gmt":"2022-03-25T20:08:22","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/union-and-intersection-of-sets-examples-venn-diagram-representation-and-faqs\/"},"modified":"2025-05-16T14:01:35","modified_gmt":"2025-05-16T08:31:35","slug":"union-and-intersection-of-sets-examples-venn-diagram-representation-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/","title":{"rendered":"Union and Intersection of Sets &#8211; Examples, Venn Diagram, Representation 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\/union-and-intersection-of-sets\/#Union_and_Intersection\" title=\"Union and Intersection\">Union and Intersection<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Union\" title=\"Union\">Union<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Intersection\" title=\"Intersection\">Intersection<\/a><\/li><\/ul><\/li><\/ul><\/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\/union-and-intersection-of-sets\/#Union_and_Intersection_Venn_Diagrams\" title=\"Union and Intersection Venn Diagrams\">Union and Intersection Venn Diagrams<\/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\/union-and-intersection-of-sets\/#Union_of_Set_Theory\" title=\"Union of Set Theory\">Union of Set Theory<\/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\/union-and-intersection-of-sets\/#Venn_Diagram_of_Union_of_Sets\" title=\"Venn Diagram of Union of Sets\">Venn Diagram of Union of Sets<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Intersection_of_Sets\" title=\"Intersection of Sets\">Intersection of Sets<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Intersection_of_Two_Sets_Representation\" title=\"Intersection of Two Sets Representation\">Intersection of Two Sets Representation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Cardinal_Number_of_Set\" title=\"Cardinal Number of Set\">Cardinal Number of Set<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Difference_between_Union_and_Intersection_of_Set\" title=\"Difference between Union and Intersection of Set\">Difference between Union and Intersection of Set<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Union_and_Intersection_Examples\" title=\"Union and Intersection Examples\">Union and Intersection Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Union_and_Intersection_of_Sets_Cardinal_Number_Practice_Problems\" title=\"Union and Intersection of Sets Cardinal Number Practice Problems\">Union and Intersection of Sets Cardinal Number Practice Problems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Union_And_Intersection\" title=\"Union And Intersection\">Union And Intersection<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/#Infinity_Learn_App\" title=\"Infinity Learn App\">Infinity Learn App<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Union_and_Intersection\"><\/span><span style=\"font-size: 18pt;\">Union and Intersection<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h4><span class=\"ez-toc-section\" id=\"Union\"><\/span><span style=\"font-size: 14pt;\"><strong>Union<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Union and Intersection of Sets.<\/p>\n<p>The union of two sets A and B is the set of all elements that are in either A or B, or both A and B. In symbols.<\/p>\n<p>A \u222a B = {x : x \u2208 A or x \u2208 B}<\/p>\n<p>For example, the union of the sets {1, 2, 3} and {4, 5, 6} is<\/p>\n<p>{1, 2, 3, 4, 5, 6}<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Intersection\"><\/span><span style=\"font-size: 14pt;\"><strong>Intersection<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The intersection of two sets A and B is the set of all elements that are in both A and B. In symbols,<\/p>\n<p>A \u2229 B = {x : x \u2208 A and x \u2208 B}<\/p>\n<p>For example, the intersection of the sets {1, 2, 3} and {4, 5, 6} is<\/p>\n<p>{4, 5, 6}<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156331 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/union-and-intersection-of-sets-examples-venn-diagram-representation-and-faqs.jpg\" alt=\"union and intersection\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/union-and-intersection-of-sets-examples-venn-diagram-representation-and-faqs.jpg?v=1648238899 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/union-and-intersection-of-sets-examples-venn-diagram-representation-and-faqs-300x212.jpg?v=1648238899 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Union_and_Intersection_Venn_Diagrams\"><\/span>Union and Intersection Venn Diagrams<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A <span style=\"color: #0000ff;\">Venn diagram<\/span> is a graphical tool that can be used to visualize the relationships between different sets. In a Venn diagram, each set is represented by a circle, and the circles are overlapping or intersecting. The overlapping areas represent the relationships between the sets.<\/p>\n<p>There are two basic types of Venn diagrams: union diagrams and intersection diagrams. In a union diagram, the circles represent sets, and the overlapping area represents the union of the sets. In an intersection diagram, the circles represent sets, and the overlapping area represents the intersection of the sets.<\/p>\n<p>Union diagrams are used to visualize the relationships between different sets of data. For example, you could use a union diagram to visualize the relationships between different types of animals. The circles could represent different types of animals, and the overlapping area would represent the animals that are both mammals and birds.<\/p>\n<p>Intersection diagrams are used to visualize the relationships between different sets of data. For example, you could use an intersection diagram to visualize the relationships between different types of fruits. The circles could represent different types of fruits, and the overlapping area would represent the fruits that are both apples and oranges.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Union_of_Set_Theory\"><\/span><span style=\"font-size: 18pt;\">Union of Set Theory<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics, set theory is the study of sets, which are collections of objects. In set theory, a set is defined as a collection of objects that can be identified by a unique name. Sets can be finite or infinite, and they can be composed of other sets. The basic operations that can be performed on sets are addition, subtraction, multiplication, and division.<\/p>\n<p>The union of two sets is the set of all objects that are members of either set. The intersection of two sets is the set of all objects that are members of both sets. The difference of two sets is the set of all objects that are members of the first set, but not the second set. The Cartesian product of two sets is the set of all objects that are members of both sets, and for each object in the first set, there is a corresponding object in the second set.<\/p>\n<p>The most important property of sets is the principle of inclusion and exclusion. This principle states that a set is a subset of another set if and only if every object in the first set is also a member of the second set. In other words, the second set includes all of the objects in the first set, and no other objects.<\/p>\n<p>Set theory is a powerful tool for mathematical analysis, because it allows us to create models of abstract concepts. For example, we can use set theory to model the real world by modeling sets of objects as sets of sets. We can also use set theory to study the properties of sets, and to develop new mathematical theories.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Venn_Diagram_of_Union_of_Sets\"><\/span><span style=\"font-size: 18pt;\">Venn Diagram of Union of Sets<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A = {1, 2, 3, 4}<\/p>\n<p>B = {2, 3, 4}<\/p>\n<p>C = {1, 3, 5}<\/p>\n<p>Union of A and B: {1, 2, 3, 4, 5}<\/p>\n<p>Union of A and C: {1, 2, 3, 5}<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Intersection_of_Sets\"><\/span><span style=\"font-size: 18pt;\">Intersection of Sets<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The intersection of two sets is the set of all elements that are in both sets.<\/p>\n<p>For example, the intersection of the sets {1, 2, 3} and {4, 5, 6} is the set {4, 5, 6}.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Intersection_of_Two_Sets_Representation\"><\/span><span style=\"font-size: 18pt;\">Intersection of Two Sets Representation<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>There are a few different ways to represent the intersection of two sets. One way is to use a Venn diagram. In a Venn diagram, each set is represented by a circle, and the intersection is represented by the area where the circles overlap.<\/p>\n<p>Another way to represent the intersection of two sets is to use a list. In a list, the elements that are in both sets are listed together.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cardinal_Number_of_Set\"><\/span><span style=\"font-size: 18pt;\">Cardinal Number of Set<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A <span style=\"color: #0000ff;\">cardinal number<\/span> is a number that represents how many objects are in a set. There are six cardinal numbers: one, two, three, four, five, and six.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Difference_between_Union_and_Intersection_of_Set\"><\/span><span style=\"font-size: 18pt;\">Difference between Union and Intersection of Set<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A union is the result of combining two or more sets. The union of two sets A and B, for example, is the set of all elements that are in A or B or both. The intersection of two sets A and B, on the other hand, is the set of all elements that are in both A and B.<\/p>\n<p>The following diagram illustrates the union and intersection of two sets A and B:<\/p>\n<p>The union of A and B is {1, 2, 3, 4, 5, 6}<\/p>\n<p>The intersection of A and B is {3, 4, 5}<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Union_and_Intersection_Examples\"><\/span><span style=\"font-size: 14pt;\">Union and Intersection Examples<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>1. Union: The union of two sets A and B, written A \u222a B, is the set of all elements that are in either A or B or both. For example, the union of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3, 4, 5, 6}.<\/p>\n<p>2. Intersection: The intersection of two sets A and B, written A \u2229 B, is the set of all elements that are in both A and B. For example, the intersection of the sets {1, 2, 3} and {4, 5, 6} is the set {4, 5}.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Union_and_Intersection_of_Sets_Cardinal_Number_Practice_Problems\"><\/span><span style=\"font-size: 14pt;\">Union and Intersection of Sets Cardinal Number Practice Problems<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>1. Find the cardinality of the set {3, 4, 5}<\/p>\n<p>3 + 4 + 5 = 12<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Union_And_Intersection\"><\/span><span style=\"font-size: 14pt;\">Union And Intersection<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Mathematically, union and intersection are two very different concepts. Union refers to the set of all elements that are in either of two given sets, while intersection refers to the set of all elements that are in both sets.<\/p>\n<p>In the real world, however, the two concepts are often confused. For example, when two people are talking about their families, they might say that their families are both united and intersecting. This is not actually true, but it can be hard to tell the difference in a conversation.<\/p>\n<p>The best way to think of union and intersection is to imagine two Venn diagrams. The circles in a Venn diagram represent sets, and the overlapping areas represent the elements that are in both sets.<\/p>\n<p>For example, imagine that you have two sets, A and B. Set A consists of the numbers 1, 2, and 3, and set B consists of the numbers 4, 5, and 6. The intersection of A and B would be the number 3, because it is the only number that is in both sets. The union of A and B would be the set of all numbers, 1, 2, 3, 4, 5, and 6.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Infinity_Learn_App\"><\/span>Infinity Learn App<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Now you can find answer to all your subject queries &amp; prepare for your Exams on our <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.infinitylearn.learn\" target=\"_blank\" rel=\"noopener\">test preparation app<\/a><\/span> &#8211; Infinity Learn.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Union and Intersection Union Union and Intersection of Sets. The union of two sets A and B is the set [&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":"Union and Intersection of Sets","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about union and intersection of sets topic of maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/union-and-intersection-of-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>Union and Intersection of Sets - Examples, Venn Diagram, Representation and FAQs - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about union and intersection of sets topic of maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/union-and-intersection-of-sets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Union and Intersection of Sets - 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