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Prove or disprove the following: (a) Let f : A → B and g : B...

Prove or disprove the following:

(a) Let f : A → B and g : B → C be two functions. If g is onto, then g ◦ f : A → C is onto.

(b) Let f : A → B and g : B → C be two functions. If g is one-to-one, then g ◦ f : A → C is one-to-one.

(c) There exist functions f : A → B and g : B → C such that f is not onto and g ◦ f : A → C is onto.

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