Set Difference Union Second Set is Union

Theorem
The union of a set difference with the second set is the union of the two sets:
 * $\left({S \setminus T}\right) \cup T = S \cup T$

Let $S, T$ be sets.

Then:
 * $\left({S \setminus T}\right) \cup T = S \cup T$

Proof
Consider $S, T \subseteq \mathbb U$, where $\mathbb U$ is considered as the universe.