Set with Complement forms Partition

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

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

Proof
Follows directly from Relative Complement Partition: if $$\varnothing \subset T \subset S$$, then $$T$$ and $$\mathcal{C}_S \left({T}\right)$$ form a partition of $$S$$.