Discrete Math Help: Proving Injectivity of f & g

[swears]

Homework Statement

f: B => C and g: A => B

1. If f of g is injective, then f is injective.

2. If f of g is injective, then g is injective.

Homework Equations

The Attempt at a Solution

I know that 1 is true and 2 is false because I found those as properties, but I am not exactly sure why, and I do not know how to show a proof.

Any help please?

 

[moo5003]

If f of g is injective then every x,y in A such that f(g(x)) = f(g(y)) implies that x=y.

I suggest from here to suppose that f or g is not injective and come up with a contradiction. Ie: suppose f is injective and g is not injective, suppose f is not injective and g is injective, suppose f and g are not injective. Work it out from here.