Suppose that n is an element ofNand φ: {1,2,..,n} --> {1,2,..,n}.

a) Prove that φ is 1-1 if and only if φ is onto.

b) Suppose that E is a finite set and f: E --> E. Prove that f is 1-1 on E if and only if f takes E onto E.

I’m thinking that this can be done by induction, but I’ve been staring at this for so long now that I can’t even get the problem started. Any hints would be greatly appreciated.