\begin{definition}[Definition:Equivalence Relation/Definition 2]
Let $\RR \subseteq S \times S$ be a relation on a set $S$.
$\RR$ is an equivalence relation {{iff}}:
:$\Delta_S \cup \RR^{-1} \cup \RR \circ \RR \subseteq \RR$
where:
:$\Delta_S$ denotes the diagonal relation on $S$
:$\RR^{-1}$ denotes the inverse relation
:$\circ$ denotes composition of relations
\end{definition}