Taken from a Practice Problems sheet with no solutions

Consider the following statements. If the statement is true, then give a proof. If the statement is false, then write out its negation and prove that.

(a) There exists a function f : Z Z + that is one-to-one and onto.

(b) For all functions g : Z + Z +, if g is one-to-one, then g is onto.

(c) For all functions h : Z Z + if h is not onto, then h is not one-to-one.

(d) There exists a function F : Z + Z + so that F is onto, but F is not one-to-one