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**ElenaS519** Here is my problem...

Let *A*, *B*, and *C* be nonempty sets and let *f: A*→*B *and *g: B*→*C* be functions.

a) Prove that if *g *∘ *f *is an injection, then *f *is an injection.

b) If *g *∘ *f *is an injection, then must *g *be an injection? Support your answer with a proof or counterexample.

c) Prove that if *g *∘ *f *is a surjection, then *g *is a surjection.

d) If *g *∘ *f *is a surjection, then must *f *be a surjection? Support your answer with a proof or a counterexpample.

Any help is greatly appreciated! Thanks!