Definition:Membership Relation

Definition
Let $S$ be a set and let $\mathcal P \left({S}\right)$ be the power set of $S$.

Let $\mathcal R \subseteq S \times \mathcal P \left({S}\right)$ be the relation defined as:
 * $\left({x, A}\right) \in \mathcal R \iff x \in A$

Thus $\mathcal R$ is the relation between elements of $S$ and subsets of $S$ expressing membership.