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Consider the relations R 1 and R 2 defined as aR 1 b ⇔ a 2 + b 2 = 1 for all a, b ∈ R and (a, b) R 2 (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N. Then :

1. Neither R 1 nor R 2 is an equivalence relation
2. Only R 2 is an equivalence relation
3. R 1 and R 2 both are equivalence relations
4. Only R 1 is an equivalence relation

Correct answer: Only R 2 is an equivalence relation

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