Power Set is Closed under Complement

Theorem
Let $S$ be a set.

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

Then:
 * $\forall A \in \powerset S: \relcomp S A \in \powerset S$

where $\relcomp S A$ denotes the complement of $A$ relative to $S$.

Also see

 * Power Set is Closed under Union
 * Power Set is Closed under Intersection
 * Power Set is Closed under Set Difference