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Set of equivalence classes

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Let X = Z × (Z {0}), and ∼ be the relation defined on X by (a, b) ∼ (c, d) whenever ad = bc. Let R = X/ ∼= {[x] : x ∈ X}, so R is the set of equivalence classes of ∼. Define the operation ⊕ on R,by setting [(a1, b1)] ⊕ [(a2, b2)] = [(a1b2 + a2b1, b1b2)]. Show that this operation is well-defined.

Reference no: EM131381851

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