{"id":9644,"date":"2022-01-20T16:24:40","date_gmt":"2022-01-20T10:54:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9644"},"modified":"2022-01-20T17:40:36","modified_gmt":"2022-01-20T12:10:36","slug":"what-is-void-or-empty-relation-with-example","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-void-or-empty-relation-with-example\/","title":{"rendered":"What is Void or Empty Relation with Example ?"},"content":{"rendered":"
Let A be a set. Then, \\(\\phi\\) \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called the void or empty relation<\/strong> on set A.<\/p>\n In other words, a relation R on a set A is called void or empty relation, if no element of A is related to any element of A.<\/p>\n Example<\/strong><\/span> : Consider the relation R on the set A = {1, 2, 3, 4, 5} defined by R = {(a, b) : a – b = 12}.<\/p>\n We observe that a – b \\(\\ne\\) 12 for any two elements of A.<\/p>\n \\(\\therefore\\) (a, b) \\(\\notin\\) R for any a, b \\(\\in\\) A.<\/p>\n \\(\\implies\\) R does not contain any element of A \\(\\times\\) A<\/p>\n \\(\\implies\\) R is empty set<\/p>\n \\(\\implies\\) R is the void relation on A.<\/p>\n","protected":false},"excerpt":{"rendered":" Solution : Let A be a set. Then, \\(\\phi\\) \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called the void or empty relation on set A. In other words, a relation R on a set A is called void or empty relation, if no element of A is …<\/p>\n