Union with Relative Complement

Theorem
The union of a set $T$ and its relative complement in $S$ is the set $S$:


 * $\complement_S \left({T}\right) \cup T = S$

Proof
From the definition of relative complement, we have that $T \subseteq S$.

From Union with Superset is Superset‎, we have that $T \subseteq S \iff S \cup T = S$, from which the result follows.