Set with Complement forms Partition

Theorem
Let $$\varnothing \subset S \subset \mathbb{U}$$.

Then $$S$$ and its complement $$\complement \left({S}\right)$$ form a partition of the universal set $$\mathbb{U}$$.

Proof
Follows directly from Relative Complement Partition: if $$\varnothing \subset T \subset S$$, then $$\left\{{T, \complement_S \left({T}\right)}\right\}$$ is a partition of $$S$$.