What is the Identity Relation with Examples ?

Solution :

Let A be a set. Then, the relation \(I_A\) = {(a, a) : a \(\in\) A} on A is called the identity relation on A.

In other words, then the relation \(I_A\) on A is called the identity relation if every element of A is related to itself only.

Example : If A = {1, 2, 3}, then the relation \(I_A\) = {(1, 1), (2, 2) (3, 3)} is the identity relation on set A. But, relations \(R_1\) = {(1, 1), (2, 2)} and \(R_2\) = {(1, 1), (2, 2), (3, 3), (1, 3)} are not identity relations on A, because (3, 3) \(\notin\) \(R_1\) and in \(R_2\) element 1 is related to elements 1 and 3.

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