Let X be the set of equivalence classes. So X = {[(a,b)] : a ∈ Z,b...

Let X be the set of equivalence classes. So X = {[(a,b)] : a ∈ Z,b ∈ N} (recall that [(a,b)] = {(c,d) ∈Z×N : (a,b) ∼ (c,d)}).

We deﬁne an addition and a multiplication on X as follows: [(a,b)] + [(c,d)] = [(ad + bc,bd)] and [(a,b)]·[(c,d)] = [(ac,bd)]

Prove that this addition and multiplication is well-deﬁned on X.

Expert Solution

Colby Messinger answered 2 years ago

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