Example 5 Show that the relation R in the set Z of integers given by
R = {(a, b) : 2 divides a – b}
is an equivalence relation Solution R is reflexive, as 2 divides (a – a) for all a ∈ Z Further, if (a, b) ∈ R, then
2 divides a – b Therefore, 2 divides b – a