Image of Union under Relation

Theorem
Let $\mathcal R \subseteq S \times T$ be a relation.

The image of the union of subsets of $S$ is equal to the union of their images.

Let $S_1$ and $S_2$ be subsets of $S$.

Then $\mathcal R \left({S_1 \cup S_2}\right) = \mathcal R \left({S_1}\right) \cup \mathcal R \left({S_2}\right)$.