# Definition:Membership Relation

## Definition

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.

## Also see

• Results about the membership relation can be found here.