Let N be the set of all natural numbers and let R be a relation in N x

1.	Let N be the set of all natural numbers and let R be a relation in N x N defined by (a, b) R (c, d) ⇔ ad = bc For all (a, b), (c, d) ∈ N x N. Show that R is an equivalence relation on N x N.
Answer» Prove it is reflexive, prove it is symmetric, prove it is transitive. Because it is reflexive, symmetric and transitive, so R is an equivalence relation on N x N.

Let N be the set of all natural numbers and let R be a relation in N x N defined by (a, b) R (c, d) ⇔ ad = bc For all (a, b), (c, d) ∈ N x N. Show that R is an equivalence relation on N x N.

Answer»

Prove it is reflexive, prove it is symmetric, prove it is transitive.

Because it is reflexive, symmetric and transitive, so R is an equivalence relation on N x N.

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Let N be the set of all natural numbers and let R be a relation in N x N defined by (a, b) R (c, d) ⇔ ad = bc For all (a, b), (c, d) ∈ N x N. Show that R is an equivalence relation on N x N.

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