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Show that the relation R in the set N x N defined by (a,b) R (c,d) if a^2 + d^2 =b^2 + c^2 ∀ a, b, c, d ∈ N, is an equivalence relation.

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Show that the relation R in the set N x N defined by (a,b) R (c,d) if a2 + d2 =b2 + c2 ∀ a, b, c, d ∈ N, is an equivalence relation.

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1 Answer

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Hence, R is transitive

Since, R is reflexive, symmetric and transitive.

Therefore, R is an equivalence relation.

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