hi

I am trying to prove the following theorem.

Suppose A,B,C are sets and $\displaystyle f:B\longrightarrow C$

Suppose that $\displaystyle A\neq \varnothing$ and for all functions $\displaystyle g\;$and

$\displaystyle h$ from $\displaystyle A\longrightarrow B$

$\displaystyle [(f\circ g=f\circ h)\Rightarrow (g=h)] $

Prove that $\displaystyle f$ is one-to-one.

Since a universal statement about functions g and h is given , I think we are

supposed to exploit this. I am not able to come up with functions g and h suitable for the situation. Can anybody give some hints ?