if f and g are surjective, then f o g is surjective. Solution Let me explain in a bit more detail : Let fog : A -> C fog is onto if, for every c in C, there exists as a in A such that fog(a) = c. But since f is onto, we have that f(b) = c for some b in B, and since g is onto, we have that b = g(x) for some x in A (I changed the letters to avoid confusion). So g(x) = b f(g(x)) = f(b) = c So this value of x exists, which is what we wanted to show. I hope this helps!.

1. if f and g are surjective, then f o g is surjective.
Solution
Let me explain in a bit more detail :
Let fog : A -> C
fog is onto if, for every c in C, there exists as a in A such that fog(a) = c.
But since f is onto, we have that f(b) = c for some b in B, and
since g is onto, we have that b = g(x) for some x in A (I changed the letters to avoid confusion).
So g(x) = b
f(g(x)) = f(b) = c
So this value of x exists, which is what we wanted to show.
I hope this helps!