Here are two important definitions related to a function f : A ? B. The function f is one-to-one (1–1) if a1=/ a2 in A implies that f(a1) =/ f(a2) in B. The function f is onto if, given any b ? B, it is possible to find an element a ? A for which f(a) = b. Give an example of each or state that the request is impossible:
(a) f : N ? N that is 1–1 but not onto.
(b) f : N ? N that is onto but not 1–1.
(c) f : N ? Z that is 1–1 and onto.