Consider each of statements about pairs of functions g : A → B and f : B → C below. The use of the phrase "any function" means that the function is not necessarily injective or surjective — it does not mean that you are allowed to change the domain or codomain of f and g. If a statement below is true, prove it using the appropriate definitions. If a statement is false, provide a counterexample.
(a) If f is injective and g is any function, then f ◦ g is injective.
(b) If f is any function and g is injective, then f ◦ g is injective.
(c) If f is injective and g is injective, then f ◦ g is injective.