# 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.