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.