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Question
Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.
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Solution
Let A be a set. Then,
Identity relation IA=IA is reflexive, since (a, a) ∈A∀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.
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