Hi

I am trying to prove the following. Suppose A and B are finite sets

and

Prove that if then is one to one iff

is onto.

I have proved one direction and I am trying to prove the other direction. i.e.

If is onto then its one to one. Here are few things which I have come up with. Since is onto

since A and B are finite with same size,

So to prove that f is one to one, should I just assume that there are two

values, such that and try to prove that

. This is the standard approach to prove that the function is one to one but I am having difficulty with this route. Can people offer any hints ?

Thanks