1. The problem statement, all variables and given/known data Let f: X ----> Y and g: Y ----> Z be functions and let h = g o f: X ----> Z 2. Relevant equations a. If h is surjective then g is surjective b. If h is surjective then f is surjective. 3. The attempt at a solution Here h: X ----> Z a. Suppose h: x ---> z is surjective for ∈ Z. Since h is surjective ∃a ∈ X such that h(a) = g(f(a)) = k Now let y = f(a) ∈ Y so... g(y) = g(f(a)) = k; as declared QED. b. Suppose h: x ---> z is surjective for y.........I'm not even sure how to start. PS: To be honest, I really need to find a good textbook on proofs because my lecturer is outright atrocious. If anyone knows of any texts, do post me some recommendations as well.