Set Difference Union First Set is First Set

Theorem
The union of a set difference with the first set is the set itself:

Let $$S, T$$ be sets.

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

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

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