Set Difference with Union

Theorem
Let $$R, S, T$$ be sets.

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

where:
 * $$R \setminus S$$ denotes set difference;
 * $$R \cup T$$ denotes set union.

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

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Then:

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Then of course:

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