Let $f: X \rightarrow Y$ and $g: Y \rightarrow X$
If $f \circ g$ is surjective, then f is surjective, too. I think that is true.
Question: How can I proove that? I have so far:
$\forall y \in Y: \exists x \in X : f(x)=y$
$\forall x \in Y : \exists y \in Y : f \circ g(y)= x$