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Let f : A → B, g : B → C be such that g ◦...

Let f : A → B, g : B → C be such that g ◦ f is one-to-one (1 : 1).

(a) Prove that f must also be one-to-one (1 : 1).

(b) Consider the statement ‘g must also be one-to-one’. If it is true, prove it. If it is not, give a counter example.

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