{"id":2077,"date":"2022-03-12T03:30:30","date_gmt":"2022-03-12T03:30:30","guid":{"rendered":"https:\/\/swatilathia.com\/?page_id=2077"},"modified":"2022-07-27T07:04:38","modified_gmt":"2022-07-27T07:04:38","slug":"operations-on-set","status":"publish","type":"page","link":"https:\/\/swatilathia.com\/?page_id=2077","title":{"rendered":"Operations on Set"},"content":{"rendered":"<body>\n<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<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69e1f3aebebb1\" class=\"ez-toc-cssicon-toggle-label\"><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><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69e1f3aebebb1\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Union_of_Sets\" >Union of Sets<\/a><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:\/\/swatilathia.com\/?page_id=2077\/#Properties_of_Union_of_Sets\" >Properties of Union of Sets<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Intersection_of_Sets\" >Intersection of Sets<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Properties_of_Intersection_of_Sets\" >Properties of Intersection of Sets<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Examples_of_Union_and_Intersection\" >Examples of Union and Intersection<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Complement_of_a_Set\" >Complement of a Set<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Properties_of_Complement_of_Set\" >Properties of Complement of Set<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Examples_of_Complement_of_Sets\" >Examples of Complement of Sets<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Difference_of_Two_Sets\" >Difference of Two Sets<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Properties_of_Difference_of_Sets\" >Properties of Difference of Sets<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Symmetric_Difference_Set\" >Symmetric Difference Set<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Properties_of_Symmetric_Difference_Sets\" >Properties of Symmetric Difference Sets<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Order_Pair\" >Order Pair<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Cartesian_Product\" >Cartesian Product<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/swatilathia.com\/?page_id=2077\/#Properties_of_Cartesian_Product\" >Properties of Cartesian Product<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Union_of_Sets\"><\/span>Union of Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">The union of two sets  A &amp; B is the set consisting of all the elements which belong to either A or B or both.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">The union of set A &amp; B  is denoted by A U B , read as A union B.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>A U B = {x \/ x \u2208 A or x \u2208 B or x \u2208 both A &amp; B}<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Venn diagram for Union of Set A &amp; B is drawn below. A U B is indicated by blue color.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Venn Diagram | Union of Sets\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/wwyJfZ_fqik?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/i2.wp.com\/www.worksheetsbuddy.com\/wp-content\/uploads\/2020\/11\/Union-of-Sets.gif?resize=290%2C179&amp;ssl=1\" alt=\"\" loading=\"lazy\"><figcaption><strong>A U B<\/strong><\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Union_of_Sets\"><\/span>Properties of Union of Sets<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>A \u2282 (A U B) and B \u2282 (A U B)<\/li><li>A U \u03a6 = A, for every set A<\/li><li>A U A = A, for every set A<\/li><li>A U B = B U A (Commutative Property)<\/li><li>(A U B) U C = A U (B U C) (Associative Property)<\/li><li>If B \u2282 A then A U B = A &amp; if A \u2282 B then A U B = B<\/li><li>A U B = \u03a6<strong> <\/strong>  =&gt; A = \u03a6 &amp; B = \u03a6 <\/li><li><a href=\"https:\/\/swatilathia.com\/distribution-law-video-tutorial\/#Proof_Distribution_Law_of_Union_over_Intersection_A_U_B_%E2%88%A9_C_A_U_B_%E2%88%A9_A_U_C\">A U (B \u2229 C) = (A U B) \u2229 (A U C) (Distributive Law of Union over Intersection)<\/a><\/li><li>If A \u2282 B &amp; C \u2282 D then (A U B) \u2282 (B U D)<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Properties Of Union of Sets | Part 1\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/SPqMsu8pTD8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Properties of Union of Sets | Part 2\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/JxkAm47K8WY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Intersection_of_Sets\"><\/span>Intersection of Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">The intersection of two sets A &amp; B is the set consisting of all elements which belong to both the set A &amp; B<\/p>\n\n\n\n<p class=\"has-medium-font-size\">The intersection of A &amp; B is denoted by A \u2229 B, read as A intersection B.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>A \u2229 B = {x \/ x \u2208 A &amp; x \u2208 B}<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Venn diagram for Intersection of Set A &amp; B is drawn below. A \u2229 B is indicated by blue color.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/math24.net\/images\/set-operations2.svg\" alt=\"\" width=\"276\" height=\"182\" loading=\"lazy\"><figcaption><strong>A \u2229 B<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Intersection of Sets\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/4ZoPxds_pm8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Intersection_of_Sets\"><\/span>Properties of Intersection of Sets<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>(A \u2229 B) \u2282 A and (A \u2229 B) \u2282 B<\/li><li>A \u2229 \u03a6 = \u03a6, for every set A<\/li><li>A \u2229 A = A, for every set A<\/li><li>A \u2229 B = B \u2229 A (Commutative Property)<\/li><li>(A \u2229 B) \u2229 C = A \u2229 (B \u2229 C) (Associative Property)<\/li><li>If B \u2282 A then A \u2229 B = B &amp; if A \u2282 B then A \u2229 B = A<\/li><li>If A \u2282 B &amp; B \u2282 C then A \u2282 (B \u2229 C) <\/li><li><a href=\"https:\/\/swatilathia.com\/distribution-law-video-tutorial\/#Proof_Distribution_Law_of_Intersection_over_Union_A_%E2%88%A9_B_U_C_A_%E2%88%A9_B_U_A_%E2%88%A9_C\">A \u2229 (B U C) = (A \u2229 B) U (A \u2229 C) (Distributive Law of Intersection over Union)<\/a><\/li><li>If A \u2282 B &amp; C \u2282 D then (A \u2229 B) \u2282 (B \u2229 D)<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Properties of Intersection of Sets | Property 1 to 4\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/H6Pdz4iKmhc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Properties of Intersection of Sets | Property 5 to 8\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/Q6NtE11MJ10?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Examples_of_Union_and_Intersection\"><\/span>Examples of Union and Intersection<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Example of Union and Intersection of sets\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/ruIELNsHzzo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Example | Find Set A , B and C\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/EGrXhM0ILOQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Complement_of_a_Set\"><\/span>Complement of a Set<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">The complement of any set is the set of all those elements which do not belong to that set itself. <\/p>\n\n\n\n<p class=\"has-medium-font-size\">If U is the universal set &amp; A \u2208 P(U), then complement of set A is the set U \u2013 A &amp; is denoted by A\u2019.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>A\u2019 = {x \/ x \u2208 U, x \u2209 A}<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Venn diagram for Complement of Set A is drawn below. A\u2019 is indicated by purple color.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/i1.wp.com\/www.worksheetsbuddy.com\/wp-content\/uploads\/2020\/11\/Complement-of-a-Set.gif?resize=300%2C187&amp;ssl=1\" alt=\"\" width=\"289\" height=\"180\" loading=\"lazy\"><figcaption><strong>A\u2019<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Disjoint Sets | Complement of a Set\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/jeCa5_yAocU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Complement_of_Set\"><\/span>Properties of Complement of Set<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>A \u2229 A\u2019 = \u03a6<\/li><li>A U A\u2019 = U (Universal set)<\/li><li>U\u2019 = \u03a6<\/li><li>\u03a6\u2019 = U<\/li><li>(A\u2019)\u2019 = A<\/li><li>If A \u2282 B then B\u2019 \u2282 A\u2019<\/li><li>(A \u2229 B) U (A \u2229 B\u2019)=A<\/li><li><a href=\"https:\/\/swatilathia.com\/distribution-law-video-tutorial\/#Complement_of_a_Intersection_is_the_Union_of_Complements\">(A \u2229 B)\u2019 = A\u2019 U B\u2019 (De Morgan\u2019s Law)<\/a><\/li><li><a href=\"https:\/\/swatilathia.com\/distribution-law-video-tutorial\/#Complement_of_a_Union_is_the_Intersection_of_Complements\">(A U B)\u2019 = A\u2019 \u2229 B\u2019 (De Morgan\u2019s Law)<\/a><\/li><\/ol>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Properties of Complement of a set | Properties 1 to 6\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/_uOWYsViXcc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Properties of Complement of a Set | Property 7 to 9\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/4aX7CrM34QM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Examples_of_Complement_of_Sets\"><\/span>Examples of Complement of Sets<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Examples of Complement of Set\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/ExCDG_EZacE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Difference_of_Two_Sets\"><\/span>Difference of Two Sets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">The difference of two sets A &amp; B is the set of all those elements which belong to set A but not set B. It is denoted by A \u2013 B &amp; read as A difference B.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>A \u2013 B = {x \/ x \u2208 A but x \u2209 B}<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Similarly, the difference of two sets B &amp; A is denoted by B \u2013 A.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>B \u2013 A = {x \/ x \u2208 B but x \u2209 A}<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">The Difference of two sets can  be shown below in shaded region by Venn diagram.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/math24.net\/images\/set-operations3.svg\" alt=\"\" width=\"232\" height=\"153\" loading=\"lazy\"><figcaption><strong>A \u2013 B<\/strong><\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Difference_of_Sets\"><\/span>Properties of Difference of Sets<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>A \u2013 B \u2282 A &amp; B \u2013 A \u2282 B<\/li><li>A \u2013 B, A \u2229 B, B \u2013 A are mutually disjoint sets.<\/li><li>A \u2013 (A \u2013 B) = A \u2229 B &amp; B \u2013 (B \u2013 A) = A \u2229 B<\/li><li>If A = B =&gt;(A \u2013 B) = \u03a6<\/li><li>A \u2013 B = A \u2229 B\u2019<\/li><li>A \u2013 \u03a6 = A<\/li><li>A \u2282 B =&gt;A \u2013 B = \u03a6<\/li><li>U \u2013 A = A\u2019<\/li><li>A U B = (A \u2013 B) U B<\/li><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Symmetric_Difference_Set\"><\/span>Symmetric Difference Set<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">A difference set is called a Symmetric Difference of two sets if it contains all those elements which are in set A, but not in set B or those which are in set B but not in set A.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">It is the union of two different set A &amp; B. It is denoted by A \u0394 B = (A \u2013 B) U (B \u2013 A)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>A \u0394 B = {x \/ x  \u2208  A or x  \u2208  B but x \u2209 A &amp; B}<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">The Symmetric difference of two sets can  be shown below in shaded region by Venn diagram.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.thoughtco.com\/thmb\/z7Dc8kkBd6k2TfiuYkmhqW70NHs%3D\/768x0\/filters%3Ano_upscale%28%29%3Amax_bytes%28150000%29%3Astrip_icc%28%29%3Aformat%28webp%29\/symmetric-56a8fa9f5f9b58b7d0f6ea14.jpg?resize=315%2C152&#038;ssl=1\" alt=\"\" width=\"315\" height=\"152\" loading=\"lazy\"><figcaption><strong>A \u0394 B<\/strong><\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Symmetric_Difference_Sets\"><\/span>Properties of Symmetric Difference Sets<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>A \u0394 B = B \u0394 A<\/li><li>A \u0394 A = \u03a6<\/li><li>A \u0394 (A \u2229 B) = A \u2013 B<\/li><li>(A \u0394 B) U (A \u2229 B) =  A U B<\/li><li>A \u0394 B = (A U B) \u2013 (A \u2229 B)<\/li><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Order_Pair\"><\/span>Order Pair<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">An order pair of two elements x &amp; y written in bracket (x, y) such that one element, say x is designated as first member &amp; y as the second member. For example :<\/p>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>The natural number &amp; their squares can be written by order pair, (1, 1), (2, 4), (3, 9), (4, 16)\u2026<\/li><li>The point on 2-dimension graph can be represented by an order pair (x, y), where x is the first co-ordinate of x-axis &amp; y is the second co-ordinate of y-axis.<\/li><li>Two order pairs (p, q) &amp; (x, y) will be equal if and only if, p = x &amp; q = y.<\/li><\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cartesian_Product\"><\/span>Cartesian Product<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">If A &amp; B be any two non empty sets, then the set of all ordered pair whose first element belong to set A &amp; second element belong to set B is called the Cartesian Product of A &amp; B in that order. It is denoted by A X B.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Symbolically, <strong>A X B = {(x, y) : x \u2208 A and y \u2208 B}<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Cartesian_Product\"><\/span>Properties of Cartesian Product<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>Though the number of elements in set A &amp; B are same, A X B \u2260 B X A<\/li><li>A X B = B X A if and only if A = B<\/li><li>If the number of elements in set A is x &amp; in set B is y then the number of elements in product set A X B are xy.<\/li><\/ol>\n\n\n\n<p><\/p>\n<\/body>","protected":false},"excerpt":{"rendered":"<p>Union of Sets The union of two sets A &amp; B is the set consisting of all the elements which belong to either A or B or both. The union of set A &amp; B is denoted by A U B , read as A union B. Symbolically, A U B = {x \/ x [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-2077","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2077","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2077"}],"version-history":[{"count":23,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2077\/revisions"}],"predecessor-version":[{"id":2542,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2077\/revisions\/2542"}],"wp:attachment":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2077"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}