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.

Also see

 * Intersection with Complement