Let φ : Q → Q be defined by φ(x) = 5 − 2x for x ∈ Q. a) Show that φ is one to one and onto. b) Is φ a homomorphism from the binary structure hQ, +i to hQ, +i? c) Give the definition of a binary operation ∗ on Q such that φ is an isomorphism mapping hQ, +i onto hQ, ∗i.

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