(A) Show That the Relation $$R = \{ ( x , y ) \mid x - y \text { is an even integer } \}$$

Essay

(a) Show that the relation $$R = \{ ( x , y ) \mid x - y \text { is an even integer } \}$$ is an equivalence relation on the set of real numbers.
(b) What are the equivalence classes of $1 \text { and } \frac { 1 } { 2 } \text { with respect to } R \text { ? }$