Question: The map : Z Z defined by (n) = n + 1 for n Z is one to one and onto Z. Give

The map ∅: Z → Z defined by ∅(n) = n + 1 for n ∈ Z is one to one and onto Z. Give the definition of a binary operation * on Z such that ∅ is an isomorphism mapping
a. (Z, •) onto (Z, *),

b. (Z, *) onto (Z, ·).
In each case, give the identity element for * on Z.

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