I am trying to prove the following. Suppose A and B are finite sets
Prove that if then is one to one iff
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 ?