Show that the Relation R defined on N x N such that (a, b) R (c, d) if only if ad = bc
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In N x N, show that the relation defined by (a, b) R (c, d) if and only if a d = b c is an equivalence relation. ... ⇒ a f = b e ⇒ (a, b) R (e, f) ∴ relation R is transitive Now R is reflexive, symmetric and transitive ∴ relation R is an equivalence relation.
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