3. Let A be a finite set. In this exertise functions f, g will be of type g: A→A and f: A → A. (a) For A = {1,2,3,4} define functions f and g, such that f is surjective and g is injective. (b) From (a) write down functions fog and gof, and determine whether they are surjective and/or injective. (c) Independently from the choices of (a), prove that function f is surjective if and only if it is injective.

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