{"id":9669,"date":"2022-01-21T17:05:34","date_gmt":"2022-01-21T11:35:34","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9669"},"modified":"2022-01-21T17:07:49","modified_gmt":"2022-01-21T11:37:49","slug":"what-is-symmetric-relation-definition-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-symmetric-relation-definition-and-examples\/","title":{"rendered":"What is Symmetric Relation – Definition and Examples"},"content":{"rendered":"

Here you will learn what is symmetric relation on sets with definition and examples.<\/p>\n

Let’s begin –<\/p>\n

What is Symmetric Relation ?<\/h2>\n

Definition<\/strong> : A relation R on a set A is said to be a symmetric relation iff<\/p>\n

\n

(a, b) \\(\\in\\) R \\(\\implies\\) (b, a) \\(\\in\\) R for all a, b \\(\\in\\) A <\/p>\n

i.e. a R b  \\(\\implies\\)  b R a for all a, b \\(\\in\\) A.<\/p>\n<\/blockquote>\n

Note<\/strong> :<\/p>\n

(i) The identity and the universal relations on a non-void set are symmetric relations.<\/p>\n

(ii) A relation R on the set A is not a symmetric relation if there are at least two elements a, b \\(\\in\\) A such that (a, b) \\(\\in\\) R but (b, a) \\(\\in\\) R.<\/p>\n

Also Read<\/strong> : Types of Relations in Math<\/a><\/p>\n

Given below are some symmetric relation examples.<\/p>\n

Example<\/strong><\/span> : Let A = {1, 2, 3, 4} and let \\(R_1\\) and \\(R_2\\) be relations on A given by \\(R_1\\) = {(1, 3),(1, 4),(3, 1),(2, 2),(4, 1)} and \\(R_2\\) = {(1, 1),(2, 2),(3, 3),(1, 3)}. Clearly, \\(R_1\\) is a symmetric relation on A. However, \\(R_2\\) is not so, because (1, 3) \\(\\in\\) \\(R_2\\) but (3, 1) \\(\\notin\\) \\(R_2\\).<\/p>\n

Example<\/strong><\/span> : Let S be a non-void set and R be a relation defined on power set P(S) by (A, B) \\(\\in\\) R \\(\\iff\\) A \\(\\subseteq\\) B for all A, B \\(\\in\\) P(S). Then, R is not a symmetric relation.<\/p>\n

Note<\/strong> : A reflexive relation on a set A is not necessarily symmetric. For example, the relation R = {(1, 1),(2, 2),(3, 3),(1, 3)} is a reflexive relation on set A = {1, 2, 3} but it is not symmetric.<\/p>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is symmetric relation on sets with definition and examples. Let’s begin – What is Symmetric Relation ? Definition : A relation R on a set A is said to be a symmetric relation iff (a, b) \\(\\in\\) R \\(\\implies\\) (b, a) \\(\\in\\) R for all a, b \\(\\in\\) A  i.e. …<\/p>\n

What is Symmetric Relation – Definition 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":[17],"tags":[580,777,778],"yoast_head":"\nWhat is Symmetric Relation - Definition and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is symmetric relation on sets with definition 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\/what-is-symmetric-relation-definition-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is Symmetric Relation - 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