(i) Since |a – a| is even,
∴ (a, a) ∈ R ∴ R is reflexive.
(ii) Let (a, b) ∈ R Then |a – b| is even
∴ |b – a| is even
∴ (b, a) ∈ R ∴ R is symmetric.
(iii) Let (a, b), (b, c) ∈ R
Then a – b = ±2m, b – c = ±2n
∴ a – c = ±2(m + n), where m, n are integers.
∴ (a, c) ∈ R ∴ R is transitive
Thus, R is an equivalence relation.