Question

PROVE THAT EVERY IDENTITY RELATION ON A SET IS REFLEXIVE BUT THE CONVERSE IS NOT NECESSARILY TRUE

Answer 1

Solution:

The relation of identity is plainly reflexive but there are some relations that are in fact reflexive but might not have been identity.

Consider the relation:
'x' won at Delhi ↔ 'y' lost at Pune. This is a reflexive relation (on the domain of people), because in fact everybody in the world has it to him- or herself.

But it need not have been, and it would not have been if the player of Delhi had not also lost at Pune. But it is reflexive.

Hence every identity relation on a set is reflexive but the converse is not necessarily true.

(Answer)