Surjectivity of Function Compositions
I am trying to prove this statement:
If $f: A \rightarrow B$ and $g: B \rightarrow C$ are both surjective functions, show that $g \circ f : A \rightarrow C$ is also a surjective function.
I know that some elements B have corresponding elements in A and likewise, some elements in C have corresponding elements in B. Is it enough to say that some elements in C must therefore correspond in A, which is what surjective function, $g \circ f : A \rightarrow C$, would show?