{"id":154498,"date":"2022-03-25T23:36:06","date_gmt":"2022-03-25T18:06:06","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/"},"modified":"2024-05-06T14:46:37","modified_gmt":"2024-05-06T09:16:37","slug":"operation-on-sets-intersection-of-sets-and-difference-of-two-sets","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/","title":{"rendered":"Set Operations"},"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\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#What_is_the_Data_Set\" title=\"What is the Data Set?\">What is the Data Set?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Notation\" title=\"Notation\">Notation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Representation_of_A_Set\" title=\"Representation of A Set\">Representation of A Set<\/a><\/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\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Types_of_Sets\" title=\"Types of Sets\">Types 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-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Union_of_Sets\" title=\"Union of Sets\">Union of Sets<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-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-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Difference_of_Sets\" title=\"Difference of Sets\">Difference of Sets<\/a><\/li><\/ul><\/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\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Properties_of_Set_Operations\" title=\"Properties of Set Operations\">Properties of Set Operations<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Union_of_Sets-2\" title=\"Union of Sets\">Union of Sets<\/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\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#Intersection_of_Sets-2\" title=\"Intersection of Sets\">Intersection of Sets<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>The set operations are the union, intersection, and difference of sets. The union of two sets is the set of all elements that are in either set. The intersection of two sets is the set of all elements that are in both sets. The difference of two sets is the set of all elements that are in the first set but not in the second set.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Data_Set\"><\/span>What is the Data Set?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The data set is a table that includes the percentage of people who are obese in each U.S. state in 2011.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Notation\"><\/span>Notation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The notation used in this problem is the standard mathematical notation for a vector. A vector is a set of numbers, usually represented by an arrow, that has a magnitude (length) and a direction. In this problem, the vector is represented by the three numbers (5, -2, 3), which represent the magnitude and direction of the vector.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Representation_of_A_Set\"><\/span>Representation of A Set<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A set is a collection of objects. The objects in a set can be anything: numbers, letters, colors, shapes, etc.<\/p>\n<p>There are two ways to represent a set:<\/p>\n<p>1. List the objects in the set<\/p>\n<p>2. Use a symbol to represent the set<\/p>\n<p>Listing the Objects in a Set<\/p>\n<p>If we want to list the objects in a set, we use a comma-separated list.<\/p>\n<p>For example, the set {1, 2, 3} can be written as:<\/p>\n<p>1, 2, 3<\/p>\n<p>or<\/p>\n<p>1, 2, 3<\/p>\n<p>Using a Symbol to Represent a Set<\/p>\n<p>If we want to use a symbol to represent a set, we use a curly bracket.<\/p>\n<p>For example, the set {1, 2, 3} can be written as:<\/p>\n<p>{1, 2, 3}<\/p>\n<p>or<\/p>\n<p>{1, 2, 3}<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Sets\"><\/span>Types of Sets<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three types of sets:<\/p>\n<p>1. Finite sets<\/p>\n<p>2. Infinite sets<br \/>\n3. Ordered sets<\/p>\n<p>Finite sets are sets that have a finite number of elements. Infinite sets are sets that have an infinite number of elements. Ordered sets are sets that have a specific order to their elements.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Union_of_Sets\"><\/span>Union of Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The union of two sets is the set of all elements that are in either set.<\/p>\n<p>The union of set A and set B is the set {x | x \u2208 A or x \u2208 B}.<\/p>\n<p>For example, the union of the set of numbers 1, 2, and 3 is the set {1, 2, 3}.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Intersection_of_Sets\"><\/span>Intersection of Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The intersection of two sets is the set that contains all the 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=\"Difference_of_Sets\"><\/span>Difference of Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The difference of two sets is the set of all elements that are in the first set but not in the second set.<\/p>\n<p>For example, the difference of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3}.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Set_Operations\"><\/span>Properties of Set Operations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Union<\/p>\n<p>The union of two sets is the set of all elements that are in either set.<\/p>\n<p>Example:<\/p>\n<p>The union of the sets {1, 2, 3} and {4, 5, 6} is the set {1, 2, 3, 4, 5, 6}.<\/p>\n<p>Intersection<\/p>\n<p>The intersection of two sets is the set of all elements that are in both sets.<\/p>\n<p>Example:<\/p>\n<p>The intersection of the sets {1, 2, 3} and {4, 5, 6} is the set {4, 5}.<\/p>\n<p>Complement<\/p>\n<p>The complement of a set is the set of all elements that are not in the set.<\/p>\n<p>Example:<\/p>\n<p>The complement of the set {1, 2, 3} is the set {4, 5, 6}.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Union_of_Sets-2\"><\/span>Union of Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8220;The union of sets is the set of all elements that are in either set.&#8221;<\/p>\n<p>The union of two sets, A and B, is the set of all elements that are in either set A or set B. The union of A and B is written as A \u222a B.<\/p>\n<p>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<h3><span class=\"ez-toc-section\" id=\"Intersection_of_Sets-2\"><\/span>Intersection of Sets<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","protected":false},"excerpt":{"rendered":"<p>The set operations are the union, intersection, and difference of sets. The union of two sets is the set of [&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":"Set Operations","_yoast_wpseo_title":"Set Operations - Formula, Properties, Examples - Infinity Learn","_yoast_wpseo_metadesc":"Learn about Operation on Sets Intersection of Sets and Difference of Two Sets topic of Maths in detail on infinitylearn.com.","custom_permalink":"maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-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>Set Operations - Formula, Properties, Examples - Infinity Learn<\/title>\n<meta name=\"description\" content=\"Learn about Operation on Sets Intersection of Sets and Difference of Two Sets topic of Maths in detail 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\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Set Operations - Formula, Properties, Examples - Infinity Learn\" \/>\n<meta property=\"og:description\" content=\"Learn about Operation on Sets Intersection of Sets and Difference of Two Sets topic of Maths in detail on infinitylearn.com.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T18:06:06+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-06T09:16:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Set Operations - Formula, Properties, Examples - Infinity Learn","description":"Learn about Operation on Sets Intersection of Sets and Difference of Two Sets topic of Maths in detail on infinitylearn.com.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/","og_locale":"en_US","og_type":"article","og_title":"Set Operations - Formula, Properties, Examples - Infinity Learn","og_description":"Learn about Operation on Sets Intersection of Sets and Difference of Two Sets topic of Maths in detail on infinitylearn.com.","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T18:06:06+00:00","article_modified_time":"2024-05-06T09:16:37+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/","name":"Set Operations - Formula, Properties, Examples - Infinity Learn","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-03-25T18:06:06+00:00","dateModified":"2024-05-06T09:16:37+00:00","description":"Learn about Operation on Sets Intersection of Sets and Difference of Two Sets topic of Maths in detail on infinitylearn.com.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Set Operations"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Set Operations","datePublished":"2022-03-25T18:06:06+00:00","dateModified":"2024-05-06T09:16:37+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/operation-on-sets-intersection-of-sets-and-difference-of-two-sets\/#webpage"},"wordCount":602,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/154498"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=154498"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/154498\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=154498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=154498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=154498"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=154498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}