I am having difficulties understanding how to build proofs and my instructor only puts some of them on the board, but never explains how he knows what to do to work proofs. I have an idea of how to build the proofs I am asking a question on, but am unsure how much information needs to be included. Please let me know how to build the following proof.
Let f: A--->B and g: B--->A be functions where A & B are given sets. Prove that:
a) f is injective if (g o f)(a)=a for all a elements in set A.
b) f is surjective if (f o g)(b)=b for all b elements in set B.