{"id":31770,"date":"2023-07-12T15:32:11","date_gmt":"2023-07-12T15:32:11","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31770"},"modified":"2023-07-12T17:59:26","modified_gmt":"2023-07-12T17:59:26","slug":"complement-of-a-set-definition-properties-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set","title":{"rendered":"Complement of a Set &#8211; Definition, Properties, Examples, Facts, 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-9aa6ca6e-206f-4c2b-a983-c9dbd3a05ca3\" 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\/complement-of-a-set#0-what-is-the-complement-of-a-set>What Is the Complement of a Set?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set#1-definition-of-complement-of-a-set>Definition of Complement of a Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set#5-properties-of-the-complement-of-a-set>Properties of the Complement of a Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set#10-solved-examples-on-the-complement-of-a-set>Solved Examples on the Complement of a Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set#11-practice-problems-on-complement-of-a-set>Practice Problems on Complement of a Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set#12-frequently-asked-questions-about-the-complement-of-a-set>Frequently Asked Questions about the Complement of a Set<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-complement-of-a-set\">What Is the Complement of a Set?<\/h2>\n\n\n\n<p><strong>In set theory, the complement of a set is the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/sets\"><strong>set<\/strong><\/a><strong> of all elements that belong to the universal set but not to the original set.<\/strong><\/p>\n\n\n\n<p>The complement of a set A is denoted by A&#8217; or Ac.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>Universal set $= U =$ Set of all <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/integers\">integers<\/a>\u00a0<\/p>\n\n\n\n<p>$U = \\left\\{&#8230;, -\\;3,\\;-\\;2,\\;-\\;1,\\; 0,\\; 1,\\; 2,\\; 3,&#8230;\\right\\}$<\/p>\n\n\n\n<p>Let A be the set of even integers.<\/p>\n\n\n\n<p>$A = \\left\\{&#8230;,\\;-\\;2,\\; 0,\\; 2,\\; 4,&#8230;\\right\\}$<\/p>\n\n\n\n<p>Here, the complement of A is the set of odd integers.<\/p>\n\n\n\n<p>Complement of set $A = A&#8217; = \\left\\{&#8230;,\\;-\\;3,\\; -\\;1,\\; 1,\\; 3,&#8230;\\right\\}$<\/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\/compare-the-sets-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\/count_comp_comp_grps_1_pt.png\" alt=\"Compare the Sets 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\">Compare the Sets 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\/count-out-the-objects-from-a-set\" 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\/count_comp_count_out_w10_pt.png\" alt=\"Count Out the Objects from a Set 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\">Count Out the Objects from a Set 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\/make-the-sets-of-objects-equal\" 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\/count_comp_eql_grps_pt.png\" alt=\"Make the Sets of Objects Equal 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\">Make the Sets of Objects Equal 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\/rearrange-groups-to-make-a-set-bigger\" 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\/count_comp_rearrange_grps_pt.png\" alt=\"Rearrange Groups to Make a Set Bigger 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\">Rearrange Groups to Make a Set Bigger 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\/set-quarter-hours-on-an-analog-clock\" 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\/time_qrtr_hrs_set_time_words_pt.png\" alt=\"Set Quarter Hours on an Analog Clock 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\">Set Quarter Hours on an Analog Clock 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\/set-the-time-after-an-interval\" 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\/time_set_time_interval_pt.png\" alt=\"Set the Time after an Interval 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\">Set the Time after an Interval 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\/set-the-time\" 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\/time_set_time_pt.png\" alt=\"Set the Time 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\">Set the Time 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\/set-time-in-half-hours\" 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\/time_set_time_half_hours_pt.png\" alt=\"Set Time in Half Hours 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\">Set Time in Half Hours 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\/set-time-in-hours\" 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\/time_set_time_hours_pt.png\" alt=\"Set Time in Hours 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\">Set Time in Hours 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\/set-time-on-an-analog-clock\" 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\/time_5_mins_set_time_ac_pt.png\" alt=\"Set Time on an Analog Clock 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\">Set Time on an Analog Clock 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 = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-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                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"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=\"1-definition-of-complement-of-a-set\">Definition of Complement of a Set<\/h2>\n\n\n\n<p>The difference between the universal set U and set A is called the complement of that set A.<\/p>\n\n\n\n<p>If U is a universal set and A be any subset of U, then the complement of A is the set of all members of the universal set U, which are not the elements of A.&nbsp;<\/p>\n\n\n\n<p>Mathematically, the complement of a set A with respect to a universal set U is defined as&nbsp;<\/p>\n\n\n\n<p>$A&#8217; = \\left\\{x \\in U : x \\in A\\right\\}$<\/p>\n\n\n\n<p>The complement of A is the set of all elements x in U that are not in A.<\/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\/find-fraction-of-a-set-of-objects\" 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\/find-fraction-of-a-set-of-objects.jpeg\" alt=\"Find Fraction of a Set of Objects 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\/find-fraction-of-a-set\" 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\/find-fraction-of-a-set.jpeg\" alt=\"Find Fraction of a Set 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\/represent-a-set-of-data\" 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\/represent-a-set-of-data.jpeg\" alt=\"Represent a Set of Data 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\/set-time-on-analog-clock\" 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\/set-time-on-analog-clock.jpeg\" alt=\"Set Time on Analog Clock 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\/set-time-on-the-clock\" 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\/set-time-on-the-clock.jpeg\" alt=\"Set time on the Clock 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\/values-of-sets-of-bills\" 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\/values-of-sets-of-bills.jpeg\" alt=\"Values of Sets of Bills 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\/write-the-value-of-a-set-of-coins\" 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\/write-the-value-of-a-set-of-coins.jpeg\" alt=\"Write the Value of a Set of Coins 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><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                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"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-complement-of-a-set-symbol\">Complement of a Set Symbol<\/h2>\n\n\n\n<p>The complement of the set A is denoted as A&#8217; or A<sup>c<\/sup> . The notation of the complement of a set uses an apostrophe (&#8216;) or a superscript c after the name of the set.&nbsp;<\/p>\n\n\n\n<p>Also, as we know that the complement of A is the difference between Universal set and the set A, we can write<\/p>\n\n\n\n<p>$A&#8217; = U\\;-\\;A$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-complement-of-a-set-venn-diagram\">Complement of a Set: Venn Diagram<\/h2>\n\n\n\n<p>A universal set is typically represented using a rectangular box. Subsets of the universal set are generally represented by a circle. The complement of a set is the region of the universal set outside the set A.<\/p>\n\n\n\n<p>The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/venn-diagram\">Venn diagram<\/a> of the complement of set A is shown below. Here, the shaded portion in yellow shows the complement of set A.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"318\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/venn-diagram-of-the-complement-of-a-set.png\" alt=\"Venn diagram of the complement of a set\" class=\"wp-image-31776\" title=\"Venn diagram of the complement of a set\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/venn-diagram-of-the-complement-of-a-set.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/venn-diagram-of-the-complement-of-a-set-300x154.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>If we have two sets that intersect each other, the complements of sets can be represented as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"557\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/complement-of-set-a-and-b.png\" alt=\"Complement of set A and B\" class=\"wp-image-31777\" title=\"Complement of set A and B\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/complement-of-set-a-and-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/complement-of-set-a-and-b-300x270.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-cardinality-of-the-complement-of-a-set\">Cardinality of the Complement of a Set<\/h2>\n\n\n\n<p>Let the cardinality of the set A be n(A), the cardinality of the universal set U be n(U), then the cardinality of the complement of A, which is represented by n(A\u2019) or |A\u2019| is given by<\/p>\n\n\n\n<p>$n(A\u2019) = n(U) \\;-\\; n(A)$<\/p>\n\n\n\n<p>$|A&#8217;| = |U| \\;-\\; |A|$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-properties-of-the-complement-of-a-set\">Properties of the Complement of a Set<\/h2>\n\n\n\n<p>Let\u2019s discuss the properties of the complement of a set.<\/p>\n\n\n\n<p><strong>Complement Laws<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The union of a set A and its complement A&#8217; is equal to the universal set U.<\/li>\n<\/ul>\n\n\n\n<p>$A \\cup A&#8217; = U$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The intersection of set A and A&#8217; is the empty set<\/li>\n<\/ul>\n\n\n\n<p>$A \\cap A\u2019 = \u2205$<\/p>\n\n\n\n<p><strong>Law of Double Complementation<\/strong><\/p>\n\n\n\n<p>The complement of the complement of a set A is equal to A itself.<\/p>\n\n\n\n<p>$(A&#8217;)&#8217; = A$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-law-of-empty-set-and-universal-set\">Law of Empty Set and Universal Set<\/h2>\n\n\n\n<p>An empty set or null set (\u2205) is the complement of the universal set. The universal set is the complement of the empty set.<\/p>\n\n\n\n<p>$\u2205&#8217; = U$<\/p>\n\n\n\n<p>$U\u2019 = \u2205$<\/p>\n\n\n\n<p><strong>De Morgan\u2019s Laws<\/strong><\/p>\n\n\n\n<p>De Morgan&#8217;s laws are a set of two fundamental laws in a set theory that relate the complement of set operations. They are named after the mathematician Augustus De Morgan, a British mathematician .<\/p>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-158f9659-ad96-47c1-83a3-00ab9d3bd9f2\">\n\n\n<ul class=\"wp-block-list\">\n<li>The complement of the union of two sets A and B is equal to the intersection of their complements.<\/li>\n<\/ul>\n\n\n\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>$(A \\cup B)&#8217; = A&#8217; \\cap B&#8217;$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The complement of the intersection of two sets A and B is equal to the union of their complements.<br>$(A \\cap B)&#8217; = A&#8217; \\cup B&#8217;$<\/li>\n<\/ul>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"7-how-to-find-the-complement-of-a-set\">How to Find the Complement of a Set<\/h2>\n\n\n\n<p>To find the complement of a set, follow the steps mentioned below:<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Write the elements of the universal set. Write down all the elements in the original set.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Find the difference between U and A. In other words, identify all the elements in the Universal set that do not belong to the original set.&nbsp;<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>The elements identified in step 3 form the complement of the set.<\/p>\n\n\n\n<p><strong>Example: <\/strong>$U = \\left\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\right\\}$<\/p>\n\n\n\n<p>$A = \\left\\{1, 3, 5, 7, 9\\right\\}$<\/p>\n\n\n\n<p>$A\u2019 = U\\;-\\;A = \\left\\{ 2, 4, 6, 8, 10\\right\\}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-facts-about-the-complement-of-a-set\">Facts about the Complement of a Set<\/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>The complement of an empty set is the universal set.<\/li>\n\n\n\n<li>The complement of a universal set is the empty set.<\/li>\n\n\n\n<li>The set and its complement are disjoint sets.<\/li>\n\n\n\n<li>The complement of a set is unique.<\/li>\n\n\n\n<li>The cardinality of a complement of a set is the difference between the cardinality of the universal set and the cardinality of the given set.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have discussed the complement of a set, the notation, the Venn diagram, the properties of the complement of a set, and the method to find the complement. Let\u2019s solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-solved-examples-on-the-complement-of-a-set\">Solved Examples on the Complement of a Set<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Let set <\/strong>$B = \\left\\{\\text{Monday, Tuesday, Wednesday, Friday}\\right\\}$<strong>. Find the complement of B.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>$B = \\left\\{\\text{Monday, Tuesday, Wednesday, Friday}\\right\\}$.<\/p>\n\n\n\n<p>Here, $U =$ Set of all days in a week<\/p>\n\n\n\n<p>$U = \\left\\{\\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}\\right\\}$<\/p>\n\n\n\n<p>Let\u2019s find the complement of B.<\/p>\n\n\n\n<p>$B&#8217; = U\\;-\\;B$<\/p>\n\n\n\n<p>$B&#8217; = \\left\\{x | x \\text{is a day of the week and x is not in B}\\right\\}$<\/p>\n\n\n\n<p>$B&#8217; = \\left\\{\\text{Thursday, Saturday, Sunday}\\right\\}$.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>Let <\/strong>$Y = \\left\\{x | x \\text{is a positive even integer}\\right\\}$<strong>. Find the complement of Y, if U is the set of positive integers.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>$Y = \\left\\{x | x \\text{is a positive even integer}\\right\\}$<\/p>\n\n\n\n<p>Here, U is the set of positive integers.<\/p>\n\n\n\n<p>Therefore, $Y&#8217; = \\left\\{x | x \\text{is a positive integer and x is odd}\\right\\}$\u00a0<\/p>\n\n\n\n<p>$Y&#8217; = \\left\\{1,\\; 3,\\; 5,\\; 7,\\; 9, &#8230;\\right\\}$.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>If <\/strong>$U = \\left\\{1,\\; 2,\\; 3,\\; 4,\\; 5,\\; 6,\\; 7,\\; 8,\\; 9,\\; 10\\right\\}$<strong> and <\/strong>$A = \\left\\{2,\\; 3,\\; 5,\\; 7\\right\\}$<strong>. Find the complement of A.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$U = \\left\\{1,\\; 2,\\; 3,\\; 4,\\; 5,\\; 6,\\; 7,\\; 8,\\; 9,\\; 10\\right\\}$<\/p>\n\n\n\n<p>$A = \\left\\{2,\\; 3,\\; 5,\\; 7\\right\\}$<\/p>\n\n\n\n<p>$\\therefore A&#8217; = U \\;-\\; A = \\left\\{1,\\; 4,\\; 6,\\; 8,\\; 9,\\; 10\\right\\}$<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>If <\/strong>$B = \\left\\{x: x \\text{is a vowel in English alphabets}\\right\\}$<strong>, then find B&#8217;.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$B = \\left\\{ x : x \\text{is a vowel in English alphabets.}\\right\\}$<\/p>\n\n\n\n<p>$B = \\left\\{a,\\; e,\\; i,\\; o,\\; u\\right\\}$<\/p>\n\n\n\n<p>$B&#8217; = \\left\\{\\text{b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}\\right\\}$<\/p>\n\n\n\n<p>$B&#8217;= \\left\\{x: x \\text{is not a vowel in English alphabets.}\\right\\}$<\/p>\n\n\n\n<p>$B&#8217; = \\left\\{x: x \\text{is a consonant in English alphabets.}\\right\\}$<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><strong>Let <\/strong>$U = \\left\\{1,\\; 2,\\; 3,\\; 4,\\; 5,\\; 6,\\; 7,\\; 8,\\; 9\\right\\}$<strong>. If <\/strong>$A = \\left\\{1,\\; 2,\\; 3\\right\\}$<strong> and <\/strong>$B = \\left\\{4,\\; 5,\\; 6\\right\\}$<strong> and <\/strong>$C = \\left\\{7,\\; 8,\\; 9\\right\\}$<strong>, then find (A U B U C)\u2019.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$A = \\left\\{1,\\; 2,\\; 3\\right\\}$ and $B = \\left\\{4,\\; 5,\\; 6\\right\\}$ and $C = \\left\\{7,\\; 8,\\; 9\\right\\}$<\/p>\n\n\n\n<p>$A U B U C = \\left\\{1,\\; 2,\\; 3,\\; 4,\\; 5,\\; 6,\\; 7,\\; 8,\\; 9\\right\\} = U$<\/p>\n\n\n\n<p>$\\therefore (A U B U C)\u2019 = U\u2019 = \u2205$\u00a0<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li><strong>If <\/strong>$U = {1,\\; 2,\\; 3,\\; 4,\\; 5}$<strong> and <\/strong>$C = \\left\\{1,\\; 3,\\; 5\\right\\}$<strong> then find (C&#8217;)&#8217;?<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$(C&#8217;)&#8217; = C$<\/p>\n\n\n\n<p>$U = \\left\\{1,\\; 2,\\; 3,\\; 4,\\; 5\\right\\}$ and $C = \\left\\{1,\\; 3,\\; 5\\right\\}$<\/p>\n\n\n\n<p>$C\u2019 = \\left\\{2,\\; 4\\right\\}$<\/p>\n\n\n\n<p>Again taking the complement of C\u2019, we get<\/p>\n\n\n\n<p>$\\therefore (C&#8217;)&#8217; = \\left\\{2,\\; 4\\right\\}&#8217; = \\left\\{1,\\;3,\\;5\\right\\} = C$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-practice-problems-on-complement-of-a-set\">Practice Problems on Complement of a Set<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Complement of a Set - Definition, Properties, Examples, Facts, 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\">$A \\cup A' =$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A<\/div><div class=\"spq_answer_block\" data-value=\"1\">A'<\/div><div class=\"spq_answer_block\" data-value=\"2\">U<\/div><div class=\"spq_answer_block\" data-value=\"3\">\u2205<\/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: U<br\/>$A \\cup A' = U$<\/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\">If $U = \\left\\{a,\\; b,\\; c,\\; d,\\; e,\\; f\\right\\}$ and $B = \\left\\{a,\\; c,\\; e\\right\\}$, what is the complement of B?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left\\{a,\\; b,\\; d,\\; f\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\left\\{a, b, c, d, e, f\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">The empty set<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\left\\{b, d, f\\right\\}$<\/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: $\\left\\{b, d, f\\right\\}$<br\/>The complement of B consists of all elements in the universal set that are not in B. \r\n$B\u2019 = \\left\\{b, d, f\\right\\}$.<br><\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">$U\u2019 =$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left\\{0\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\u2205$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left\\{1\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">U<\/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: $\u2205$<br\/>$U\u2019 = \u2205$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If $U = \\left\\{a,\\; b\\right\\}$ and the set $D = \\left\\{b\\right\\}$, what is the complement of D?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left\\{a, b\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\left\\{a\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left\\{b\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\u2205$<\/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: $\\left\\{a\\right\\}$<br\/>$U = \\left\\{a,\\; b\\right\\}$<br>\r\n$D = \\left\\{b\\right\\}$<br>\r\n$D\u2019 =  U\\;-\\;D = \\left\\{a\\right\\}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">$(A \\cup B)' =$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$A' \\cup B'$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$A' \\cap B'$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$A \\cup B$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$A \\cap B$<\/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: $A' \\cap B'$<br\/>By De Morgan\u2019s law, $(A \\cup B)'= A' \\cap B'$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Complement of a Set - Definition, Properties, Examples, Facts, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Complement of a Set\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$A \\\\cup A' =$$\",\n                    \"text\": \"$$A \\\\cup A' =$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$A \\\\cup A' = U$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A \\\\cup A' = U$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A'\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A \\\\cup A' = U$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2205\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A \\\\cup A' = U$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"U\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$A \\\\cup A' = U$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$A \\\\cup A' = U$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$U = \\\\left\\\\{a,\\\\; b,\\\\; c,\\\\; d,\\\\; e,\\\\; f\\\\right\\\\}$$ and $$B = \\\\left\\\\{a,\\\\; c,\\\\; e\\\\right\\\\}$$, what is the complement of B?\",\n                    \"text\": \"If $$U = \\\\left\\\\{a,\\\\; b,\\\\; c,\\\\; d,\\\\; e,\\\\; f\\\\right\\\\}$$ and $$B = \\\\left\\\\{a,\\\\; c,\\\\; e\\\\right\\\\}$$, what is the complement of B?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The complement of B consists of all elements in the universal set that are not in B. \r\n$$B\u2019 = \\\\left\\\\{b, d, f\\\\right\\\\}$$.<br>\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{a,\\\\; b,\\\\; d,\\\\; f\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The complement of B consists of all elements in the universal set that are not in B. \r\n$$B\u2019 = \\\\left\\\\{b, d, f\\\\right\\\\}$$.<br>\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{a, b, c, d, e, f\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The complement of B consists of all elements in the universal set that are not in B. \r\n$$B\u2019 = \\\\left\\\\{b, d, f\\\\right\\\\}$$.<br>\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The empty set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The complement of B consists of all elements in the universal set that are not in B. \r\n$$B\u2019 = \\\\left\\\\{b, d, f\\\\right\\\\}$$.<br>\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left\\\\{b, d, f\\\\right\\\\}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The complement of B consists of all elements in the universal set that are not in B. \r\n$$B\u2019 = \\\\left\\\\{b, d, f\\\\right\\\\}$$.<br>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The complement of B consists of all elements in the universal set that are not in B. \r\n$$B\u2019 = \\\\left\\\\{b, d, f\\\\right\\\\}$$.<br>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$U\u2019 =$$\",\n                    \"text\": \"$$U\u2019 =$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$U\u2019 = \u2205$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{0\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$U\u2019 = \u2205$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{1\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$U\u2019 = \u2205$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"U\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$U\u2019 = \u2205$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\u2205$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$U\u2019 = \u2205$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$U\u2019 = \u2205$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$ and the set $$D = \\\\left\\\\{b\\\\right\\\\}$$, what is the complement of D?\",\n                    \"text\": \"If $$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$ and the set $$D = \\\\left\\\\{b\\\\right\\\\}$$, what is the complement of D?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$<br>\r\n$$D = \\\\left\\\\{b\\\\right\\\\}$$<br>\r\n$$D\u2019 =  U\\\\;-\\\\;D = \\\\left\\\\{a\\\\right\\\\}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{a, b\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$<br>\r\n$$D = \\\\left\\\\{b\\\\right\\\\}$$<br>\r\n$$D\u2019 =  U\\\\;-\\\\;D = \\\\left\\\\{a\\\\right\\\\}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{b\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$<br>\r\n$$D = \\\\left\\\\{b\\\\right\\\\}$$<br>\r\n$$D\u2019 =  U\\\\;-\\\\;D = \\\\left\\\\{a\\\\right\\\\}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\u2205$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$<br>\r\n$$D = \\\\left\\\\{b\\\\right\\\\}$$<br>\r\n$$D\u2019 =  U\\\\;-\\\\;D = \\\\left\\\\{a\\\\right\\\\}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left\\\\{a\\\\right\\\\}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$<br>\r\n$$D = \\\\left\\\\{b\\\\right\\\\}$$<br>\r\n$$D\u2019 =  U\\\\;-\\\\;D = \\\\left\\\\{a\\\\right\\\\}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$U = \\\\left\\\\{a,\\\\; b\\\\right\\\\}$$<br>\r\n$$D = \\\\left\\\\{b\\\\right\\\\}$$<br>\r\n$$D\u2019 =  U\\\\;-\\\\;D = \\\\left\\\\{a\\\\right\\\\}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$(A \\\\cup B)' =$$\",\n                    \"text\": \"$$(A \\\\cup B)' =$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"By De Morgan\u2019s law, $$(A \\\\cup B)'= A' \\\\cap B'$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$A' \\\\cup B'$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By De Morgan\u2019s law, $$(A \\\\cup B)'= A' \\\\cap B'$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$A \\\\cup B$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By De Morgan\u2019s law, $$(A \\\\cup B)'= A' \\\\cap B'$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$A \\\\cap B$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By De Morgan\u2019s law, $$(A \\\\cup B)'= A' \\\\cap B'$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$A' \\\\cap B'$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By De Morgan\u2019s law, $$(A \\\\cup B)'= A' \\\\cap B'$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By De Morgan\u2019s law, $$(A \\\\cup B)'= A' \\\\cap B'$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-frequently-asked-questions-about-the-complement-of-a-set\">Frequently Asked Questions about the Complement of a Set<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-c012da55-51e2-4821-8a84-65ab2dff8387\" 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-c012da55-51e2-4821-8a84-65ab2dff8387\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c012da55-51e2-4821-8a84-65ab2dff8387\"><strong>What is the meaning of a complement 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-c012da55-51e2-4821-8a84-65ab2dff8387\">\n\n<p>The meaning of a complement set is the set of all elements in the universal set that are not in the given set.<\/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-c012da55-51e2-4821-8a84-65ab2dff8387\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c012da55-51e2-4821-8a84-65ab2dff8387\"><strong>What is the notation for the complement of a 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-1-c012da55-51e2-4821-8a84-65ab2dff8387\">\n\n<p>The symbol used to denote the complement of a set is usually an apostrophe (&#8216;) or a superscript c, placed after the set symbol. For example, if A is a set, then its complement can be denoted by A&#8217; or A<sup>c<\/sup>.<\/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-c012da55-51e2-4821-8a84-65ab2dff8387\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c012da55-51e2-4821-8a84-65ab2dff8387\"><strong>What is the formula for the complement of a 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-2-c012da55-51e2-4821-8a84-65ab2dff8387\">\n\n<p>The formula for the complement of a set A with respect to a universal set U is given byA&#8217; $= U\\;-\\;A = \\left\\{x \\in U | x \\in A\\right\\}$<\/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-3-c012da55-51e2-4821-8a84-65ab2dff8387\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c012da55-51e2-4821-8a84-65ab2dff8387\"><strong>What is the difference between a set and its complement?<\/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-3-c012da55-51e2-4821-8a84-65ab2dff8387\">\n\n<p>A set and its complement have no element in common.Thus, $A \\;-\\; A&#8217; = A$<\/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-4-c012da55-51e2-4821-8a84-65ab2dff8387\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c012da55-51e2-4821-8a84-65ab2dff8387\"><strong>What is the complement of the empty 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-4-c012da55-51e2-4821-8a84-65ab2dff8387\">\n\n<p>The complement of the empty set is the universal set.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Complement of a Set? In set theory, the complement of a set is the set of all elements that belong to the universal set but not to the original set. The complement of a set A is denoted by A&#8217; or Ac. Example: Universal set $= U =$ Set of all integers\u00a0 &#8230; <a title=\"Complement of a Set &#8211; Definition, Properties, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/complement-of-a-set\" aria-label=\"More on Complement of a Set &#8211; Definition, Properties, Examples, Facts, 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-31770","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\/31770","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=31770"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31770\/revisions"}],"predecessor-version":[{"id":31789,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31770\/revisions\/31789"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}