{"id":4043,"date":"2021-08-15T11:40:02","date_gmt":"2021-08-15T11:40:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4043"},"modified":"2022-01-16T16:56:40","modified_gmt":"2022-01-16T11:26:40","slug":"what-is-inverse-relation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-inverse-relation\/","title":{"rendered":"What is Inverse Relation – Definition and Example"},"content":{"rendered":"

Here you will learn what is inverse relation, identity relation and posets in relation with example.<\/p>\n

Let’s begin –<\/p>\n

Definition of Inverse Relation<\/h2>\n

If relation R is defined from A to B, then inverse relation would be defined form B to A, i.e.<\/p>\n

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R : A \\(\\rightarrow\\) B \\(\\implies\\) aRb where a \\(\\in\\) A, b \\(\\in\\) B<\/p>\n

\\(R^{-1}\\) : B \\(\\rightarrow\\) A \\(\\implies\\) bRa where a \\(\\in\\) A, b \\(\\in\\) B<\/p>\n<\/blockquote>\n

Domain of R = Range of \\(R^{-1}\\)<\/p>\n

and  Range of R = Domain of \\(R^{-1}\\)<\/p>\n

\\(\\therefore\\)   \\(R^{-1}\\) = {(b, a) | (a, b) \\(\\in\\) R}<\/p>\n

A relation R is defined on the set of 1st ten natural numbers.<\/p>\n

e.g.   N is a set of first 10 natural numbers.<\/p>\n

aRb \\(\\implies\\) a + 2b = 10<\/p>\n

R = {(2, 4), (4, 3), (6, 2), (8, 1)}<\/p>\n

\\(R^{-1}\\) = {(4, 2), (3, 4), (2, 6), (1, 8)}<\/p>\n

Identity Relation<\/h2>\n

A relation defined on a set A is said to be an identity relation if each and every element of A is related to itself & only to itself.<\/p>\n

e.g.  A relation defined on the set of natural numbers is<\/p>\n

aRb \\(\\implies\\) a = b where a & b \\(\\in\\) N<\/p>\n

R = {(1, 1), (2, 2), (3, 3), ……}<\/p>\n

R is an identity relation<\/p>\n

Posets<\/h2>\n

A relation R on a set P is called an partial relation order if it is reflexive, antisymmetric and transitive. That means that for all x, y and z in P we have:<\/p>\n