Question

An "Anti-symmetric" relation need not be reflexive relation: give an example.

Answer 1

The relation $R=\left\{\right(1,1),(2,3\left)\right\}$ on the set $A=\{1,2,3\}$ is an anti-symmetric relation, as the necessary condition for it is satisfied.

But it is not reflexive as $(2,2),(3,3)\notin R,$ through $(1,1),(2,2),(3,3)\in R$