Let G be a cyclic group with generator a, and let G' be a group isomorphic to G. If ∅ : G → G' is an isomorphism, show that, for every x ∈ G, ∅(x) is completely determined by the value ∅(a). That is, if ∅ : G →G' and ψ : G → G' are two isomophisms such that ∅(a) = ψ(a), then∅(x) = ψ(x) for all x ∈ G.