# Set Theory? question

1. Mar 13, 2016

### BubblesAreUs

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.

2. Mar 13, 2016

### PeroK

Your proof of a) looks quite good. You didn't say what k is, but it's fairly obvious.

Why do you think b) is true?

3. Mar 13, 2016

### BubblesAreUs

k is just an integer that belongs to set Z.

As for b, I think f is surjective because h is. Since f is an input of g, I'm not exactly sure how I can re-utilise my proof from part a.

4. Mar 13, 2016

### PeroK

If I can't see how to prove something, I usually try to disprove it and see what happens.