How would you prove the following facts:
(a) If $f\colon A \to B$ and $g \colon B \to C$ are injective then $g \circ f$ is injective.
(b) If $f\colon A \to B$ and $g \colon B \to C$ are surjective then $g \circ f$ is surjective.
(c) If $f\colon A \to B$ and $g \colon B \to C$ are bijective then $g \circ f$ is bijective.