My question is that suppose a set $A = \{1,2,3,4\}$ so, the identity relation can be $R_1 = \{(1,1), (2,2), (3,3), (4,4)\}$ but can it be $R_2 = \{(1,1), (2,2)\}$?
2026-04-03 01:53:15.1775181195
Is an identity relation unique or can there be multiple?
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No, the identity relation is reflexive: all elements stand in the identity relation to themselves (and no elements stand in the identity relation to any element other than themselves). So it is $R1$. It has to be $R1$. For any set there is one and only one identity relation.