\begin{definition}[Definition:Membership Relation]
Let $S$ be a set.
Let $\powerset S$ denote the power set of $S$.
Let $\RR \subseteq S \times \powerset S$ be the relation defined as:
:$\tuple {x, A} \in \RR \iff x \in A$
Thus $\RR$ is the relation between elements of $S$ and subsets of $S$ expressing '''membership'''.
\end{definition}