Suppose that n N and : {1. 2,..., n) {1, 2 }. a) Prove

Suppose that n ∈ N and ϕ : {1. 2,..., n) → {1, 2 «}.
a) Prove that ϕ is 1-1 if and only if ϕ is onto.
b) [PIGEONHOLE PRINCIPLE] Suppose that E is a finite set and that f : E → E. Prove that f is 1-1 on E if and only if f takes E onto £.