Proving Equivalence Relations On A Set
You have to prove that $R$ is reflexive, symmetric and transitive.
1)Reflexive:
Clear since if we have the same set then least elements are equal. So, $SRS$.
2) Symmetric:
Suppose $SRT$. Then least element of $S$ equals least element of $T$. Hence, least element of $T$ equals least element of $S$. So, $TRS$.
3) Transitive:
Suppose $SRT$ and $TRU$. Then least element of $S$ equals least element of $T$ and least element of $T$ equals least element of $U$. Hence, least element of $S$ equals least element of $U$. So, $SRU$.