Is this equivalence relation: $\{(1,2),(2,1),(1,1)\}$?

Question

Let $S=\{1,2,3\}$ and $R=\{(1,2),(2,1),(1,1)\}$ Over $S, R$ does not have pairs like $(2,2),(3,3).$ Is it reflexive even though those elements in set $S$ are not used? But it is symmetric and transitive.

Answer 1

Your relation $R$ is not an equivalence relation.

You have $(2,1)$ and $(1,2)$ but you do not have $(2,2)$ so it is not transitive. You do not have $(2,2)$ and $(3,3)$ so it is not reflexive.