Question
Check if R : Z → Z, R = {(a, b) | 2 divides a – b} is an equivalence relation.
(ii) Let (a, b) ∈ R Then 2 divides a – b ∴ 2 divides b – a ∴ (b, a) ∈ R ∴ R is symmetric.
(iii) Let (a, b) ∈ R, (b, c) ∈ R Then a – b = 2m, b – c = 2n, ∴ a – c = 2(m + n), where m, n are integers. ∴ 2 divides a – c ∴ (a, c) ∈ R ∴ R is transitive. Thus, R is an equivalence relation.
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passing through the points (-3, 1) and (2, -2).