Union with Complement

Theorem
The union of a set and its complement is the universe:


 * $$S \cup \complement \left({S}\right) = \mathbb{U}$$

Proof
Substitute $$\mathbb{U}$$ for $$S$$ and $$S$$ for $$T$$ in $$T \cup \complement_S \left({T}\right) = S$$ from Union with Relative Complement.