Union with Complement

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

$$S \cup \mathcal{C} \left({S}\right) = \mathbb{U}$$

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