Relative Complement of Relative Complement

Theorem
The relative complement of the relative complement of a set is itself:


 * $\complement_S \left({\complement_S \left({T}\right)}\right) = T$

Thus, considered as a mapping on the power set of $S$:
 * $\complement_S: \mathcal P \left({S}\right) \to \mathcal P \left({S}\right): \complement_S \left({T}\right) = S \setminus T$

$\complement_S$ is an involution.