- #1

BubblesAreUs

- 43

- 1

## Homework Statement

Let

f: X ----> Y and g: Y ----> Z

be functions and let

h = g o f: X ----> Z

## Homework Equations

a. If h is surjective then g is surjective

b. If h is surjective then f is surjective.

## 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.