Preimage of Union under Relation

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

$$\mathcal{R}^{-1} \left({C \cup D}\right) = \mathcal{R}^{-1} \left({C}\right) \cup \mathcal{R}^{-1} \left({D}\right)$$

Proof
This follows from Image of Union, and the fact that $$\mathcal{R}^{-1}$$ is itself a relation, and therefore obeys the same rules.