$S=\{(1,2), (2,1)\}:$ This relation is Irreflexive, Symmetric, Not Transitive, Not Reflexive, Not Asymmetric, Not antisymmetric.
Equivalence Relation $\implies$ Symmetric, Transitive, Reflexive.
It is not transitive & Reflexive.
Reflexive closure of $S = \{ (1,1),(2,2),(3,3),(1,2),(2,1) \}$
After taking transitive closure relation does not change.
Answer: $S = \{ (1,1),(2,2),(3,3),(1,2),(2,1)\}$
$S = \{a,b\}$
$P(S) = \{ \emptyset,{a},{b},{a,b}\}$
Related Hasse Diagram