Let  and .(a) If C0 ⊂ C. show that .(b) If f and g are injective, show that  is injective....

Let  and .

(a) If C0 ⊂ C. show that .

(b) If f and g are injective, show that  is injective.

(c) If  is injective, what can you say about injectivity of f and g?

(d) If f and g are surjective, show that  is surjective.

(e) If  is surjective, what can you say about surjectivity of f and g?

(f) Summarize your answers to (b)–(e) in the form of a theorem.