Definition:Membership Relation

Definition
Let $S$ be a set.

Let $\powerset S$ denote the power set of $S$.

Let $\mathcal R \subseteq S \times \powerset S$ be the relation defined as:
 * $\tuple {x, A} \in \mathcal R \iff x \in A$

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