Question

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

Answer 1

Let A be a set. Then,

$\mathrm{Identity}relation\mathrm{IA}=I_A\mathrm{is}\mathrm{reflexive},\mathrm{since}\left(a,a\right)\in A\forall a$

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

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