Image of Union under Relation

Theorem
Let $$\mathcal{R} \subseteq S \times T$$ be a relation. Let $$A$$ and $$B$$ be subsets of $$S$$. Then:

$$\mathcal{R} \left({A \cup B}\right) = \mathcal{R} \left({A}\right) \cup \mathcal{R} \left({B}\right)$$