# Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.

Question:

Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.

Solution:

Let A be a set. Then,

Identity relation IA $=I_{A}$ is reflexive, since $(a, a) \in A \forall a$

The converse of it need not be necessarily true.
Consider the set A = {1, 2, 3}

Here,
Relation = {(1, 1), (2, 2) , (3, 3), (2, 1), (1, 3)} is reflexive on A.
However, R is not an identity relation.