Equivalence Relation/Examples/Even Sum

Example of Equivalence Relation
Let $\Z$ denote the set of integers.

Let $\mathcal R$ denote the relation on $\Z$ defined as:
 * $\forall x, y \in \Z: x \mathrel {\mathcal R} y \iff x + y \text { is even}$

Then $\mathcal R$ is an equivalence relation.