{"id":35635,"date":"2023-11-09T16:26:30","date_gmt":"2023-11-09T16:26:30","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35635"},"modified":"2023-11-09T16:49:47","modified_gmt":"2023-11-09T16:49:47","slug":"a-intersection-b-complement-definition-formula-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement","title":{"rendered":"A Intersection B Complement &#8211; Definition, Formula, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-6994a736-9532-4bc4-abb2-ca47737fb7da\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement#0-what-is-%E2%80%98a-intersection-b-complement%E2%80%99>What Is \u2018A Intersection B Complement\u2019?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement#1-%E2%80%98a-intersection-b-complement%E2%80%99-formulas>\u2018A Intersection B Complement\u2019 Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement#3-%E2%80%98a-intersection-b-complement%E2%80%99-venn-diagram>\u2018A Intersection B Complement\u2019 Venn Diagram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement#7-solved-examples-on-%E2%80%98a-intersection-b-complement%E2%80%99>Solved Examples on \u2018A Intersection B Complement\u2019<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement#8-practice-problems-on-%E2%80%98a-intersection-b-complement%E2%80%99>Practice Problems on \u2018A Intersection B Complement\u2019<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement#9-frequently-asked-questions-about-%E2%80%98a-intersection-b-complement%E2%80%99>Frequently Asked Questions about \u2018A Intersection B Complement\u2019<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-%E2%80%98a-intersection-b-complement%E2%80%99\">What Is \u2018A Intersection B Complement\u2019?<\/h2>\n\n\n\n<p><strong>The term \u201cA intersection B complement\u201d refers to the set denoted by A \u2229 B&#8217;. It represents the elements that are in set A but not in set B. It signifies the intersection of set A with the complement of set B.&nbsp;<\/strong><\/p>\n\n\n\n<p>In other words, it includes the elements that belong to A but are not shared with B. This concept is commonly used in set theory and can help analyze relationships between different sets.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"404\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-intersection-b-complement.png\" alt=\"A intersection B complement\" class=\"wp-image-35642\" title=\"A intersection B complement\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-intersection-b-complement.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-intersection-b-complement-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>A set is defined as the collection of well-defined objects.&nbsp;<\/p>\n\n\n\n<p><strong>What is A \u22c2 B?<\/strong><\/p>\n\n\n\n<p>The intersection of two sets, indicated by &#8220;A \u2229 B&#8221;, is the collection of elements shared by both sets A and B. In other words, it contains all of the elements found in both sets.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"383\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-a-intersection-b.png\" alt=\"Venn diagram A intersection B\" class=\"wp-image-35643\" title=\"Venn diagram A intersection B\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-a-intersection-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-a-intersection-b-300x185.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>What is the complement of a set?<\/strong><\/p>\n\n\n\n<p>The complement of a set includes all elements that are not in set A but present in the universal set U. In simpler language, the complement of A comprises everything in the universal set that is not A.&nbsp;<\/p>\n\n\n\n<p>Complement of the set A = A&#8217; = A\u0305 = A<sup>C<\/sup>&nbsp;<\/p>\n\n\n\n<p>A\u2019 = U-A<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"458\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-a-complement.png\" alt=\"Venn diagram A complement\" class=\"wp-image-35644\" title=\"Venn diagram A complement\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-a-complement.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-a-complement-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Keeping these definitions in mind, we can easily understand the definition of &#8220;A Intersection B Complement&#8221; or A \u2229 B&#8217;. It denotes the set containing all elements from the set A and the complement of the set B.&nbsp;&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/10-and-100-more-than-the-same-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">10 and 100 More than the Same Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-10-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_10_number_pt.png\" alt=\"Add 10 to a 3-Digit Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 10 to a 3-Digit Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-100-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_100_horizontal_pt.png\" alt=\"Add 100 to a 3-Digit Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 100 to a 3-Digit Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-and-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit and 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-numbers-by-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit Numbers By Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_pt.png\" alt=\"Add 3 Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-in-any-order\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers in Any Order Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-groups-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Using Groups of Objects Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-%E2%80%98a-intersection-b-complement%E2%80%99-formulas\">\u2018A Intersection B Complement\u2019 Formulas<\/h2>\n\n\n\n<p>The \u2018A Intersection B Complement\u2019 formula can be defined as<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {x | x \u2208 A and x \u2209 B}<\/p>\n\n\n\n<p>We can also define the formula as<\/p>\n\n\n\n<p>A &#8211; B = A \u2229 B&#8217;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Formula<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Description<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">A \u2229 B&#8217; = A &#8211; B<\/td><td class=\"has-text-align-left\" data-align=\"left\">A Intersection B Complement is equal to the A minus B.<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">A \u2229 B&#8217; = {x | x \u2208 A and x \u2209 B}<\/td><td class=\"has-text-align-left\" data-align=\"left\">A Intersection B Complement is equal to the set containing elements in set A but not in set B.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Example<\/strong>: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5}, and B = {4, 5, 6, 7, 8}.<\/p>\n\n\n\n<p>B\u2019 = {1, 2, 3, 9, 10}<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {x | x \u2208 A and x \u2209 B}\u00a0<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {1, 2, 3} \u2026(i)<\/p>\n\n\n\n<p>Also, A &#8211; B = {1, 2, 3, 4, 5} &#8211; {4, 5, 6, 7, 8}<\/p>\n\n\n\n<p>A &#8211; B = {1, 2, 3} \u2026(ii)<\/p>\n\n\n\n<p>A \u2229 B&#8217;= A &#8211; B&nbsp;<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/10-and-100-more-than-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/10-and-100-more-than-a-3-digit-number.jpeg\" alt=\"10 and 100 More than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/100-more-and-100-less-than-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/100-more-and-100-less-than-a-3-digit-number.jpeg\" alt=\"100 More and 100 Less than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/100-more-than-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/100-more-than-a-3-digit-number.jpeg\" alt=\"100 More than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/above-and-below\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/above-and-below.jpeg\" alt=\"Above and Below Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-subtract-multiples-of-10\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" 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alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Wheel\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    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\"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-proof-for-a-%E2%88%A9-b-a-b\">Proof for A \u2229 B&#8217; = A &#8211; B<\/h2>\n\n\n\n<p>A &#8211; B represents the set that is formed by removing all the elements of A \u2229 B from the set A.<\/p>\n\n\n\n<p>Let x A \u2229 B&#8217;.<\/p>\n\n\n\n<p>\u21d4 x \u2208 A and x \u2208 B&#8217;<\/p>\n\n\n\n<p>\u21d4 x \u2208 A and x \u2209 B<\/p>\n\n\n\n<p>\u21d4 x \u2208 A but x \u2209 B<\/p>\n\n\n\n<p>\u21d4 x \u2208 (A &#8211; B)<\/p>\n\n\n\n<p>Thus, A &#8211; B = A \u2229 B&#8217;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"295\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-intersection-b-complement-equals-the-difference-of-the-sets-a-and-b.png\" alt=\"A intersection B complement equals the difference of the sets A and B\" class=\"wp-image-35645\" title=\"A intersection B complement equals the difference of the sets A and B\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-intersection-b-complement-equals-the-difference-of-the-sets-a-and-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-intersection-b-complement-equals-the-difference-of-the-sets-a-and-b-300x143.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-%E2%80%98a-intersection-b-complement%E2%80%99-venn-diagram\">\u2018A Intersection B Complement\u2019 Venn Diagram<\/h2>\n\n\n\n<p>Take a look at the Venn diagram of A intersection B complement.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"429\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-Intersection-b-complement-venn-diagram.png\" alt=\"A Intersection B complement - Venn diagram\" class=\"wp-image-35646\" title=\"A Intersection B complement - Venn diagram\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-Intersection-b-complement-venn-diagram.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-Intersection-b-complement-venn-diagram-300x208.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The shaded portion represents elements that are in set A but not in B. It defines the intersection of A and complement of B.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-a-intersection-b-whole-complement\">A Intersection B Whole Complement<\/h2>\n\n\n\n<p>We define A intersection B whole complement as (A \u2229 B)&#8217;. It represents the complement of the set (A \u2229 B). It is the complement of the intersection of sets A and B.<\/p>\n\n\n\n<p>This refers to the set of all elements in the universal set that are not present in the intersection of sets A and B. In other words, it includes all the elements that do not belong to both A and B simultaneously.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"400\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-of-a-intersection-b-whole-complement.png\" alt=\"Venn diagram of A intersection B whole complement\" class=\"wp-image-35647\" title=\"Venn diagram of A intersection B whole complement\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-of-a-intersection-b-whole-complement.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/venn-diagram-of-a-intersection-b-whole-complement-300x194.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>By the De Morgan&#8217;s Law, we have<\/p>\n\n\n\n<p>\u00a0(A \u2229 B)&#8217; = A&#8217; \u222a B&#8217;<\/p>\n\n\n\n<p>The \u201cA intersection B whole complement\u201d is equal to the union of A complement and B complement.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-facts-about-%E2%80%98a-intersection-b-complement%E2%80%99\">Facts about \u2018A Intersection B Complement\u2019<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>A Intersection B Complement has all elements present in the universal set except for the elements in A and not in B.<\/li>\n\n\n\n<li>The intersection and complement operations have significant importance in multiple areas of mathematics, such as set theory, logic, etc.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the set operation A \u2229 B&#8217;, where we explored the elements that belong to set A but not to set B. Understanding this concept is pivotal for grasping the relationships between sets. Let&#8217;s enhance our understanding by solving examples and practicing MCQs.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-%E2%80%98a-intersection-b-complement%E2%80%99\">Solved Examples on \u2018A Intersection B Complement\u2019<\/h2>\n\n\n\n<p><strong>Example 1: There are two sets, A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. What will be the <\/strong>A \u2229 B&#8217;?<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>A = {1, 2, 3, 4, 5}<\/p>\n\n\n\n<p>B = {4, 5, 6, 7, 8}<\/p>\n\n\n\n<p>A \u2229 B&#8217; = A &#8211; B<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {1, 2, 3}<\/p>\n\n\n\n<p><strong>Example 2: In set A = {Apple, Banana, Orange, Mango} and set B = {Banana, Peach, Grapefruit}. Find A Intersection B Complement.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>A = {Apple, Banana, Orange, Mango}<\/p>\n\n\n\n<p>B = {Banana, Peach, Grapefruit}<\/p>\n\n\n\n<p>A \u2229 B&#8217; = A &#8211; B<\/p>\n\n\n\n<p>A \u2229 B&#8217;= {Apple, Orange, Mango}<\/p>\n\n\n\n<p><strong>Example 3: What will be <\/strong><strong>A \u2229 B&#8217;<\/strong><strong> if A = {2, 4, 6, 8, 10}, B = {3, 6, 9}, and U = {1, 2, 3, \u2026, 10}?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>A = {2, 4, 6, 8, 10}<\/p>\n\n\n\n<p>B = {3, 6, 9}<\/p>\n\n\n\n<p>U = {1, 2, 3, \u2026, 10}<\/p>\n\n\n\n<p>B\u2019 = U &#8211; B = {1, 2, 4, 5, 7, 8, 10}<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {x | x \u2208 A and x \u2208 B&#8217;}<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {2, 4, 8, 10}<\/p>\n\n\n\n<p>A \u2229 B&#8217; = {2, 4, 8, 10}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-%E2%80%98a-intersection-b-complement%E2%80%99\">Practice Problems on \u2018A Intersection B Complement\u2019<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">A Intersection B Complement - Definition, Formula, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find A \u2229 B' of the sets A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{4, 5}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{1, 2, 3, 6, 7, 8}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{1, 2, 3}<\/div><div class=\"spq_answer_block\" data-value=\"3\">{6, 7, 8}<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: {1, 2, 3}<br\/>A \u2229 B' =  A - B = {1, 2, 3}<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">A \u2229 B'=<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A \u2229 B'={x | x \u2209 A and x \u2209 B}<\/div><div class=\"spq_answer_block\" data-value=\"1\">A \u2229 B'={x | x \u2209 A and x \u2208 B}<\/div><div class=\"spq_answer_block\" data-value=\"2\">A \u2229 B'={x | x \u2208 A and x \u2208 B}<\/div><div class=\"spq_answer_block\" data-value=\"3\">A \u2229 B'={x | x \u2208 A and x \u2209 B}<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: A \u2229 B'={x | x \u2208 A and x \u2209 B}<br\/>A \u2229 B'={x | x \u2208 A and x \u2209 B}<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">(A \u2229 B)' =<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">(A \u2229 B)'=A' U B'<\/div><div class=\"spq_answer_block\" data-value=\"1\">(A \u2229 B)'=A' \u2229 B'<\/div><div class=\"spq_answer_block\" data-value=\"2\">(A \u2229 B)'=A \u2229 B<\/div><div class=\"spq_answer_block\" data-value=\"3\">(A \u2229 B)'=A U B<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: (A \u2229 B)'=A' U B'<br\/>(A \u2229 B)'=A' U B'<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n     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\"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"(A \u2229 B)'=A' U B'\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-about-%E2%80%98a-intersection-b-complement%E2%80%99\">Frequently Asked Questions about \u2018A Intersection B Complement\u2019<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\"><strong>What is a universal set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\">\n\n<p>A universal set is a collection of all the items relevant to a specific context. It serves as a starting point for considering additional sets in that context. The universal set is a subset of all other sets under discussion. A universal set is often expressed in notation by the sign \u03be (Xi) or U.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\"><strong>What is the difference between (A \u2229 B)&#8217; or A \u2229 B&#8217;?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\">\n\n<p>(A \u2229 B)&#8217;: The complement of the intersection of sets A, and B comprises all the elements that are not shared by both sets A and B but might belong to a bigger universal set. This is also known as the complement of the intersection of A and B.<\/p>\n\n\n\n<p>A \u2229 B&#8217;: This refers to the intersection of set A with the complement of set B. It encompasses all elements that belong to set A but not set B. This is known as the intersection of A with the complement of B.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\"><strong>Is A \u2229 B&#8217; a subset of A?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-2dbedbbe-ad17-438b-ab52-9fdc3783de7e\">\n\n<p>Yes, all elements in A \u2229 B&#8217; are part of set A. They&#8217;re the elements that fulfill the criteria of being in A and not in B.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is \u2018A Intersection B Complement\u2019? The term \u201cA intersection B complement\u201d refers to the set denoted by A \u2229 B&#8217;. It represents the elements that are in set A but not in set B. It signifies the intersection of set A with the complement of set B.&nbsp; In other words, it includes the elements &#8230; <a title=\"A Intersection B Complement &#8211; Definition, Formula, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/a-intersection-b-complement\" aria-label=\"More on A Intersection B Complement &#8211; Definition, Formula, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-35635","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=35635"}],"version-history":[{"count":6,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35635\/revisions"}],"predecessor-version":[{"id":35652,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35635\/revisions\/35652"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}