Set with Complement forms Partition

Theorem

Let $\O \subset S \subset \mathbb U$.

Then $S$ and its complement $\map \complement S$ form a partition of the universal set $\mathbb U$.

Proof

Follows directly from Set with Relative Complement forms Partition:

If $\O \subset T \subset S$, then $\set {T, \relcomp S T}$ is a partition of $S$.

$\blacksquare$