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Let X, Y and Z be sets. Let f : X → Y and g :...

Let X, Y and Z be sets. Let f : X → Y and g : Y → Z functions. (a) (3 Pts.) Show that if g ◦ f is an injective function, then f is an injective function. (b) (2 Pts.) Find examples of sets X, Y and Z and functions f : X → Y and g : Y → Z such that g ◦ f is injective but g is not injective. (c) (3 Pts.) Show that if g ◦ f is a surjective function, then g is a surjective function. (d) (2 Pts.) Find examples of sets X, Y and Z and functions f : X → Y and g : Y → Z such that g ◦ f is surjective but f is not injective.

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