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.

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