I have two questions which are related to mappings as follow:
Given 3 sets E, F, and G such that $f: E \rightarrow F, g: F \rightarrow G$ are two mappings. Prove that:
a. If $g \circ f$ is injective and $f$ is surjective then $g$ is injective.
b. If $g \circ f$ is surjective and $g$ is injective then $f$ is surjective.
For these two problems. I have solved halfway for each.
For the problem (a), I have proved that $f$ is bijective.
For the problem (b), I have proved that $g$ is bijective.
I don't know how to do next because I don't find the relation to conclude.