{"id":9613,"date":"2022-01-18T00:23:42","date_gmt":"2022-01-17T18:53:42","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9613"},"modified":"2022-01-18T00:23:46","modified_gmt":"2022-01-17T18:53:46","slug":"intersection-of-sets-definition-and-venn-diagram-with-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/intersection-of-sets-definition-and-venn-diagram-with-examples\/","title":{"rendered":"Intersection of Sets – Definition and Venn Diagram with Examples"},"content":{"rendered":"

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

Let’s begin –<\/p>\n

What is the Intersection of Sets ?<\/h2>\n

Definition<\/strong> : Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and B.<\/p>\n

The intersection of A and B is denoted by \\(A \\cap B\\) (read as “A intersection B”)\"intersection<\/p>\n

Thus, \\(A \\cap B\\) = {x : x \\(\\in\\) A and x \\(\\in\\) B}.<\/p>\n

Clearly, x \\(\\in\\) \\(A \\cap B\\)  \\(\\iff\\)  x \\(\\in\\) A and x \\(\\in\\) B.<\/p>\n

In the given figure, the shaded region represents \\(A \\cap B\\). This is the venn diagram for intersection of sets<\/strong>.<\/p>\n

Evidently, \\(A \\cap B\\) \\(\\subseteq\\) A, \\(A \\cap B\\) \\(\\subseteq\\) B.<\/p>\n

Note<\/strong> : If \\(A_1\\), \\(A_2\\), …. , \\(A_n\\) is a finite family of sets, then their intersection is denoted by \\(A_1 \\cap A_2 \\cap ….. \\cap A_n\\).<\/p>\n

Example<\/strong><\/span> : If A = {1, 2, 3, 4, 5} and B = {1, 3, 9, 12}, then \\(A \\cap B\\) = {1, 3}.<\/p>\n

Example<\/strong><\/span> : If A = {1, 2, 3, 4, 5, 6, 7}, B = {2, 4, 6, 8} and C = {4, 6, 7, 8, 9, 10, 11}, then find \\(A \\cap B\\) and \\(A \\cap B \\cap C\\).<\/p>\n

Solution<\/span><\/strong> : \\(A \\cap B\\) = {2, 4, 6}<\/p>\n

\\(\\therefore\\)  \\(A \\cap B \\cap C\\) = {4, 6}<\/p>\n

Formula to Find Number of Elements in A Intersection B<\/h2>\n

If A, B and C are finite sets, and U be the finite universal set, then<\/p>\n

n(\\(A \\cap B\\)) = n(A) + n(B) – n(\\(A \\cup B\\))<\/p><\/blockquote>\n

where, n(A) = number of elements in set A<\/p>\n

n(B) = number of elements in set B<\/p>\n

n(\\(A \\cup B\\)) = number of elements in union of sets A and B<\/p>\n

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

Example<\/span><\/strong> : If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(\\(X \\cup Y\\)) = 38, then find n(\\(X \\cap Y\\)).<\/p>\n

Solution<\/strong><\/span> : By using the above formula,<\/p>\n

n(\\(X \\cap Y\\)) = n(X) + n(Y) – n(\\(X \\cup Y\\))<\/p>\n

\\(\\implies\\)  n(\\(X \\cap Y\\)) = 17 + 23 – 38<\/p>\n

\\(\\implies\\)  n(\\(X \\cap Y\\)) = 2<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the intersection of sets with definition and venn diagram and examples. Let’s begin – What is the Intersection of Sets ? Definition : Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and …<\/p>\n

Intersection of Sets – Definition and Venn Diagram with 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":[762,764,763],"yoast_head":"\nIntersection of Sets - Definition and Venn Diagram with Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the intersection of sets with definition and 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\/intersection-of-sets-definition-and-venn-diagram-with-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Intersection of Sets - 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