{"id":9684,"date":"2022-01-22T01:57:19","date_gmt":"2022-01-21T20:27:19","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9684"},"modified":"2022-01-22T01:57:20","modified_gmt":"2022-01-21T20:27:20","slug":"what-is-antisymmetric-relation-definition-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-antisymmetric-relation-definition-and-examples\/","title":{"rendered":"What is Antisymmetric Relation – Definition and Examples"},"content":{"rendered":"

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

Let’s begin –<\/p>\n

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

Definition<\/strong> : Let A be any set. A relation R on set A is said to be an antisymmetric relation iff<\/p>\n

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

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

(i)  It follows from this definition that if (a, b) \\(\\in\\) R but (b, a) \\(\\notin\\) R, then also R is an antisymmetric relation.<\/p>\n

(ii)  The identity relation on a set A is an antisymmetric relation.<\/p>\n

Also Read<\/strong> : What is Symmetric Relation \u2013 Definition and Examples<\/a><\/p>\n

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

Example<\/strong><\/span> : Let R be a relation on the set N of natural numbers defined by<\/p>\n

x R y  \\(\\iff\\)  ‘x divides y’  for all x, y \\(\\in\\) N.<\/p>\n

This relation is an antisymmetric relation on N. Since for any two numbers a, b \\(\\in\\) N.<\/p>\n

a | b and b | a \\(\\implies\\) a = b i.e. a R b and b R a \\(\\implies\\) a = b<\/p>\n

It should be noted that this relation is not antisymmetric on the set Z of integers, because we find that for any non-zero integer a, a R (-a) and (-a) R a but a \\(\\ne\\) – a.<\/p>\n

Example<\/strong><\/span> : The relation \\(\\le\\) (“less than or equal to”) on the set R of real numbers is antisymmetric, because a \\(\\le\\) b and b \\(\\le\\) a \\(\\implies\\) a = b for all a, b \\(\\in\\) R.<\/p>\n","protected":false},"excerpt":{"rendered":"

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

What is Antisymmetric 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":[782,781],"yoast_head":"\nWhat is Antisymmetric Relation - Definition and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is antisymmetric 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-antisymmetric-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 Antisymmetric Relation - 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