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Define f : N^2 Z by f(x, y) = y x for all (x, y) N^2 . (a) Show that f is

Define f : N^2 → Z by f(x, y) = y − x for all (x, y) ∈ N^2 .


(a) Show that f is surjective. (b) Let S = {(x, y) ∈ N^2 : y = 2x − 1}. 


Prove that f|S : S → Z is injective

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