{"id":9600,"date":"2022-01-18T00:23:52","date_gmt":"2022-01-17T18:53:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9600"},"modified":"2022-01-18T00:23:56","modified_gmt":"2022-01-17T18:53:56","slug":"union-of-sets-definition-and-venn-diagram-with-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/union-of-sets-definition-and-venn-diagram-with-examples\/","title":{"rendered":"Union of Sets – Definition and Venn Diagram with Examples"},"content":{"rendered":"

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

Let’s begin –<\/p>\n

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

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

We shall use the notation \\(A \\cup B\\)  (read as “A union B”) to denote the union of A and B.\"union<\/p>\n

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

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

And,  x \\(\\notin\\) \\(A \\cup B\\)  \\(\\iff\\)  x \\(\\notin\\) A   or   x \\(\\notin\\) B.<\/p>\n

In the given figure whole shaded part represents \\(A \\cup B\\). This is the venn diagram for union of sets<\/strong>.<\/p>\n

It is evident from the definition the A \\(\\subseteq\\) \\(A \\cup B\\), B\\(\\subseteq\\) \\(A \\cup B\\).<\/p>\n

If A and B are two sets such that A \\(\\subset\\) B, then \\(A \\cup B\\) = B. Also, \\(A \\cup B\\) = A, if B\\(\\subset\\) A.<\/p>\n

Example<\/strong><\/span> : If A = {1, 2, 3} and B = {1, 3, 5, 7}, then \\(A \\cup B\\) = {1, 2, 3, 5, 7}.<\/p>\n

Example<\/strong><\/span> : If A = {1, 2, 3}, B = {3, 5} and C = {4, 7, 8}. Then \\(A \\cup B \\cup C\\) = {1, 2, 3, 4, 5, 7, 8}.<\/p>\n

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

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

n(\\(A \\cup B\\)) = n(A) + n(B) – n(\\(A \\cap 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 \\cap B\\)) = number of elements in intersection 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 \\cap Y\\)) = 2, then find n(\\(X \\cup Y\\)).<\/p>\n

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

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

\\(\\implies\\)  n(\\(X \\cup Y\\)) = 17 + 23 – 2<\/p>\n

\\(\\implies\\)  n(\\(X \\cup Y\\)) = 38<\/p>\n","protected":false},"excerpt":{"rendered":"

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

Union 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":[759,761,760],"yoast_head":"\nUnion of Sets - Definition and Venn Diagram with Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the union of sets with definition and venn diagram representation 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\/union-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=\"Union of Sets - 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