{"id":9652,"date":"2022-01-20T17:41:43","date_gmt":"2022-01-20T12:11:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9652"},"modified":"2022-01-21T17:07:11","modified_gmt":"2022-01-21T11:37:11","slug":"what-is-reflexive-relation-definition-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-reflexive-relation-definition-and-examples\/","title":{"rendered":"What is Reflexive Relation – Definition and Examples"},"content":{"rendered":"

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

Let’s begin –<\/p>\n

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

Definition<\/strong> : A relation R on a set A is said to be reflexive if every element of A is related to itself.<\/p>\n

Thus, R is reflexive \\(\\iff\\) (a, a) \\(\\in\\) R for all a \\(\\in\\) A.<\/p><\/blockquote>\n

A relation R on a set A is not reflexive if there exists an element a \\(\\in\\) A such that (a, a) \\(\\notin\\) R.<\/p>\n

Note<\/strong> : The identity relation on a non-void set A is always a reflexive relation on A. However, a reflexive relation on A is not necessarily the identity relation on A. For example, the relation R = {(a, a), (b, b), (c, c), (a, b) is a reflexive relation on set A = {a, b, c} but it is not the identity relation on A.<\/p>\n

Note<\/strong> : The universal relation on a non-void set A is reflexive.<\/p>\n

Also Read<\/strong> : Identity Relation with Examples<\/a><\/p>\n

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

Example<\/strong><\/span> : Let A = {1, 2, 3} be a set. Then R = {(1, 1), (2, 2), (3, 3), (1, 3), (2, 1)} is a reflexive relation on A.<\/p>\n

But, \\(R_1\\) = {(1, 1), (3, 3), (2, 1), (3, 2)} is not a reflexive relation on A, because 2 \\(\\in\\) A  but (2, 2) \\(\\notin\\) \\(R_1\\).<\/p>\n

Example<\/strong><\/span> : Let X be a non-void set and P(X) be the power set of X. A relation R on P(X) defined by (A, B) \\(\\in\\) R \\(\\iff\\) A \\(\\subseteq\\) B is a reflexive relation since every set is subset of itself.<\/p>\n

Example <\/strong><\/span> : Let L be the set of all lines in a plane. Then relation R on  L defined by \\((l_1, l_2)\\) \\(\\in\\) R \\(\\iff\\) \\(l_1\\) is parallel to \\(l_2\\) is reflexive, since every line is parallel to itself.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is reflexive relation on set with definition and examples. Let’s begin – What is Reflexive Relation ? Definition : A relation R on a set A is said to be reflexive if every element of A is related to itself. Thus, R is reflexive \\(\\iff\\) (a, a) \\(\\in\\) R for …<\/p>\n

What is Reflexive 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":[579,776,775],"yoast_head":"\nWhat is Reflexive Relation - Definition and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is reflexive relation on set 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-reflexive-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 Reflexive Relation - 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