Answer Happy

Let f : Z × Z → Z × Z be a function defined by g(m, n) = 2− n, 3 + m).
a. Carefully prove that f is injective (one-to-one). Important!In each step of your proof make sure it is clear whether what iswritten is something you are assuming, something you are about toprove, or something that follows from a previous step. If anyvariables appear in your proof, make sure you clearly write whatthey represent.
b. Carefully prove that f is surjective (onto). Justify youranswer
Q6. Let f: Zx Z → Z × Z be a function defined by g(m, n) = (2-n, 3+ m). a. Carefully prove that f is injective (one-to-one). Important! In each step of your proof make sure it is clear whether what is written is something you are assuming, something you are about to prove, or something that follows from a previous step. If any variables appear in your proof, make sure you clearly write what they represent. b. Carefully prove that f is surjective (onto). Justify your answer! [6 points]