Relative Complement Mapping on Powerset is Bijection/Proof 1

Proof
From Relative Complement of Relative Complement:


 * $\forall X \subseteq S: \relcomp S {\relcomp S X} = X$

That is, $\complement_S$ is an involution.

The result follows from Mapping is Involution iff Bijective and Symmetric.