{"id":9633,"date":"2022-01-18T00:27:08","date_gmt":"2022-01-17T18:57:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9633"},"modified":"2022-01-18T00:27:13","modified_gmt":"2022-01-17T18:57:13","slug":"complement-of-a-set-venn-diagram-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/complement-of-a-set-venn-diagram-and-examples\/","title":{"rendered":"Complement of a Set – Venn Diagram and Examples"},"content":{"rendered":"

Here you will learn what is the complement of a set definition with venn diagram and examples.<\/p>\n

Let’s begin –<\/p>\n

Complement of a Set<\/h2>\n

Definition<\/strong> : Let U be the universal set and let A be a set such that A \\(\\subset\\) U. Then, the complement of A with respect to U is denoted by A’ or \\(A^c\\) or U – A and is defined the set of all those elements of U which are not in A.<\/p>\n

Thus, A’ = {x \\(\\in\\) U : x \\(\\notin\\) A}<\/p>\n

Clearly,  x \\(\\in\\) A’  \\(\\iff\\)  x \\(\\in\\) A.<\/p>\n

Venn Diagram :<\/h2>\n

\"complement<\/p>\n

Also Read<\/strong> : Formulas and Operation of Sets<\/a><\/p>\n

Example 1<\/strong><\/span> : Let the set of natural numbers N = {1, 2, 3, 4, ….. } be the universal set and let A = {2, 4, 6, 8, ….}. Then A’ = {1, 3, 5, ….}\/<\/p>\n

Example 2<\/span><\/strong> : If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 3, 5, 7, 9}, then A’ = {2, 4, 6, 8}.<\/p>\n

Following results are direct consequence of the definition of the complement of a set.<\/p>\n

(i)  U’ = {x \\(\\in\\) U : x \\(\\notin\\) U} = \\(\\phi\\)<\/p>\n

(ii)  \\({\\phi}’\\) = {x \\(\\in\\) U : x \\(\\notin\\) \\(\\phi\\)} = U<\/p>\n

(iii)  (A’)’ = {x \\(\\in\\) U : x \\(\\notin\\) A’} = {x \\(\\in\\) U : x \\(\\in\\) A} = A<\/p>\n

(iv)  A \\(\\cup\\) A’ = U<\/p>\n

(v)  A \\(\\cap\\) A’ = \\(\\phi\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the complement of a set definition with venn diagram and examples. Let’s begin – Complement of a Set Definition : Let U be the universal set and let A be a set such that A \\(\\subset\\) U. Then, the complement of A with respect to U is denoted by …<\/p>\n

Complement of a Set – Venn Diagram and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[16],"tags":[774,773,772],"yoast_head":"\nComplement of a Set - Venn Diagram and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the complement of a set definition with venn diagram and examples based on it.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/complement-of-a-set-venn-diagram-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Complement of a Set - 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