{"id":9646,"date":"2022-01-20T16:32:52","date_gmt":"2022-01-20T11:02:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9646"},"modified":"2022-01-20T17:40:40","modified_gmt":"2022-01-20T12:10:40","slug":"what-are-universal-relation-with-example","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-are-universal-relation-with-example\/","title":{"rendered":"What are Universal Relation with Example ?"},"content":{"rendered":"

Solution :<\/h2>\n

Let A be a set. Then, A \\(\\times\\) A \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called the universal relation on A<\/strong>.<\/p>\n

In other words, a relation R on a set is called universal relation, if each element of A is related to every element of A.<\/p>\n

Example<\/strong><\/span> : Consider the relation R on the set A = {1, 2, 3, 4, 5, 6} defined by R = {(a, b) \\(\\in\\) R : |a – b| \\(ge\\) 0}.<\/p>\n

We observe that  |a – b| \\(\\ge\\) 0 for all a, b \\(\\in\\) A<\/p>\n

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

\\(\\implies\\)  Each element of set A is related to every element of set A<\/p>\n

\\(\\implies\\)  R = A \\(\\times\\) A<\/p>\n

\\(\\implies\\)  R is universal relation on set A<\/p>\n

Note<\/strong> : It is to note here that the void relation and relation and the universal relation on a set A are respectively the smallest and the largest relations on set A. Both the empty (or void) relation and the universal relation are sometimes called trivial relations.<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let A be a set. Then, A \\(\\times\\) A \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called the universal relation on A. In other words, a relation R on a set is called universal relation, if each element of A is related to every element …<\/p>\n

What are Universal Relation with Example ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":[43,56],"tags":[],"yoast_head":"\nWhat are Universal Relation with Example ? - Mathemerize<\/title>\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-are-universal-relation-with-example\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What are Universal Relation with Example ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Let A be a set. 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