Set Difference is Subset of Union of Differences

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

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

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

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

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