f: X ----> Y and g: Y ----> Z
be functions and let
h = g o f: X ----> Z
a. If h is surjective then g is surjective
b. If h is surjective then f is surjective.
The Attempt at a Solution
h: X ----> Z
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.
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.