{"id":156142,"date":"2022-03-26T01:25:41","date_gmt":"2022-03-25T19:55:41","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/reflexive-relation\/"},"modified":"2022-12-22T21:52:25","modified_gmt":"2022-12-22T16:22:25","slug":"reflexive-relation","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/","title":{"rendered":"Reflexive Relation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#What_is_a_Reflexive_Relation\" title=\"What is a Reflexive Relation?\">What is a Reflexive Relation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#The_Property_of_Reflexive_Relations\" title=\"The Property of Reflexive Relations\">The Property of Reflexive Relations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#Number_of_Reflexive_Relationships\" title=\"Number of Reflexive Relationships\">Number of Reflexive Relationships<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#Formula_for_Number_of_Reflexive_Relations\" title=\"Formula for Number of Reflexive Relations\">Formula for Number of Reflexive Relations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#Reflexive_Relation_Characteristics\" title=\"Reflexive Relation Characteristics\">Reflexive Relation Characteristics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#Reflexive_Relation_Examples\" title=\"Reflexive Relation Examples\">Reflexive Relation Examples<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#Reflexive_Relation_Characteristics-2\" title=\"Reflexive Relation Characteristics\">Reflexive Relation Characteristics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/reflexive-relation\/#Reflexive_Relation_Examples-2\" title=\"Reflexive Relation Examples\">Reflexive Relation Examples<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Reflexive_Relation\"><\/span>What is a Reflexive Relation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A reflexive relation is a binary relation that is reflexive, meaning that every element in the set is related to itself. For example, the relation &#8220;is taller than&#8221; is reflexive, because every element in the set of people is related to itself.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156141 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/reflexive-relation.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/reflexive-relation.jpg?v=1648238138 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/reflexive-relation-300x212.jpg?v=1648238138 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Property_of_Reflexive_Relations\"><\/span>The Property of Reflexive Relations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Reflexive relations are those in which an object or element relates to itself. For example, a person&#8217;s height is a reflexive relation because a person&#8217;s height is always the same as the person&#8217;s height. Other examples of reflexive relations include a person&#8217;s weight, age, and gender.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Number_of_Reflexive_Relationships\"><\/span>Number of Reflexive Relationships<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Reflexive relationships are those in which an object is both the subject and the object of the action. For example, when a person looks in a mirror, they are looking at themselves. Similarly, when a person writes a letter to themselves, they are both the subject and the object of the action.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Formula_for_Number_of_Reflexive_Relations\"><\/span>Formula for Number of Reflexive Relations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The number of reflexive relations is the number of pairs of objects where each object is in a relation with the other object.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Reflexive_Relation_Characteristics\"><\/span>Reflexive Relation Characteristics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A reflexive relation is a relationship in which an object is both the subject and the object of the relationship. For example, in the relationship &#8220;I am writing a paper,&#8221; the object (the paper) is both the subject (the thing being written) and the object (the thing being written about). In general, reflexive relations are symmetrical; that is, the relationship is the same in both directions.<\/p>\n<p>Reflexive relations have a few important characteristics. First, reflexive relations are always transitive; that is, if A is related to B and B is related to C, then A is also related to C. Second, reflexive relations are always symmetrical; that is, the relationship is the same in both directions. Finally, reflexive relations are always reflexive; that is, the relationship always holds between the object and itself.<\/p>\n<p>Reflexive relations are important in mathematics, where they are used to define certain operations. For example, the operation of addition is defined as the reflexive relation that exists between two numbers, A and B, such that A + B = B + A. This means that the sum of two numbers is the same as the sum of the inverse of those numbers.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Reflexive_Relation_Examples\"><\/span>Reflexive Relation Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A reflexive relation is a binary relation (R) between two objects (x and y) such that xRy if and only if x = y.<\/p>\n<p>Examples of reflexive relations include &#8220;being a parent of oneself,&#8221; &#8220;being a sibling of oneself,&#8221; and &#8220;being a student of oneself.&#8221;<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Reflexive_Relation_Characteristics-2\"><\/span>Reflexive Relation Characteristics<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Some of the characteristics of a reflexive relation are listed below:<\/p>\n<ul>\n<li dir=\"ltr\" aria-level=\"1\">\n<p dir=\"ltr\" role=\"presentation\">Anti &#8211; Reflexive: If the elements of the set do not relate to themselves, they are said to be irreflexive or anti-reflexive.<\/p>\n<\/li>\n<\/ul>\n<ul>\n<li dir=\"ltr\" aria-level=\"1\">\n<p dir=\"ltr\" role=\"presentation\">Quasi-Reflexive: If each element is related to a specific component, which is also related to itself, then that relationship is called quasi-reflexive. If a set A is quasi-reflexive, this can be mathematically represented as \u2200 a, b \u2208 A: a ~ b \u21d2 (a ~ a \u2227 b ~ b).<\/p>\n<\/li>\n<\/ul>\n<ul>\n<li dir=\"ltr\" aria-level=\"1\">\n<p dir=\"ltr\" role=\"presentation\">Co-Reflexive: The relationship ~ (similar to) is co-reflexive for all elements a and b in set A if a ~ b also implies that a = b.<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\">It is impossible for a reflexive relationship on a non-empty set A to be anti-reflective, asymmetric, or anti-transitive.<\/p>\n<p dir=\"ltr\">To know more about reflexive relations, log on to <a href=\"http:\/\/student.infinitylearn.com\">Infinity Learn<\/a> and find out what the experts have to say. Understand the concepts from the easiest explanation given by the mentors and develop your conceptual foundation strongly.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Reflexive_Relation_Examples-2\"><\/span>Reflexive Relation Examples<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Example 1: A relation R on set A (set of integers) is defined by \u201cx R y if 5x + 9x is divisible by 7x\u201d for all x, y \u2208 A. Check if R is a reflexive relation on A.<\/p>\n<p dir=\"ltr\">Solution:<\/p>\n<p dir=\"ltr\">Consider x \u2208 A.<\/p>\n<p dir=\"ltr\">Now, 5x + 9x = 14x, which is divisible by 7x.<\/p>\n<p dir=\"ltr\">Therefore, x R y holds for all the elements in set A.<\/p>\n<p dir=\"ltr\">Hence, R is a reflexive relationship.<\/p>\n<p dir=\"ltr\">Example 2: A relation R is defined on the set of all real numbers N by \u2018a R b\u2019 if |a-a| \u2264 b, for a, b \u2208 N. Show that the R is not a reflexive relation.<\/p>\n<p dir=\"ltr\">Solution:<\/p>\n<p dir=\"ltr\">N is a set of all real numbers. So, b =-2 \u2208 N is possible.<\/p>\n<p dir=\"ltr\">Now |a \u2013 a| = 0. Zero is not equal to nor is it less than -2 (=b).<\/p>\n<p dir=\"ltr\">So, |a-a| \u2264 b is false.<\/p>\n<p dir=\"ltr\">Therefore, the relation R is not reflexive.<\/p>\n<p dir=\"ltr\">Example 3: A relation R on the set S by \u201cx R y if x \u2013 y is divisible by 5\u201d for x, y \u2208 A. Confirm that R is a reflexive relation on set A.<\/p>\n<p dir=\"ltr\">Solution:<\/p>\n<p dir=\"ltr\">Consider, x \u2208 S.<\/p>\n<p dir=\"ltr\">Then x \u2013 x= 0. Zero is divisible by 5.<\/p>\n<p dir=\"ltr\">Since x R x holds for all the elements in set S, R is a reflexive relation.<\/p>\n<p dir=\"ltr\">Example 4: Consider the set A in which a relation R is defined by \u2018m R n if and only if m + 3n is divisible by 4, for x, y \u2208 A. Show that R is a reflexive relation on set W.<\/p>\n<p dir=\"ltr\">Solution:<\/p>\n<p dir=\"ltr\">Consider m \u2208 W.<\/p>\n<p dir=\"ltr\">Then, m+3m=4m. 4m is divisible by 4.<\/p>\n<p dir=\"ltr\">Since x R x holds for all the elements in set W, R is a reflexive relation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is a Reflexive Relation? A reflexive relation is a binary relation that is reflexive, meaning that every element in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Reflexive Relation","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Reflexive Relation topic of Maths in details explained by subject experts on infinitylearn.com. 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