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Let R 1 = {(a, b) ∈ N × N : |a – b| ≤ 13} and R 2 = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N :

1. Both R 1 and R 2 are equivalence relations
2. Neither R 1 nor R 2 is an equivalence relation
3. R 1 is an equivalence relation but R 2 is not
4. R 2 is an equivalence relation but R 1 is not

Correct answer: Neither R 1 nor R 2 is an equivalence relation

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