Exercise 1: Let f: X →Y and g: Y → Z be two functions. (a) If f and g are injective, prove go f is injective. (b) If f and g are surjective, prove gof is surjective. (c) If gof is injective, prove f is injective. (d) If gof is surjective, prove g is surjective. (e) If gof is injective and f is surjective, prove g is injective. (f) If gof is surjective and g is injective, prove f is surjective.

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A: See the attachment

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