Question

Give example of a function f: N-> N which is:

(a) injective but not surjective.
(b) surjective but not injective.
(c) bijective but not identity function.

Answer 1

An injective function is not a function that is surjective. This means that you want a function that has a unique output for each input, that doesn't cover the natural numbers.
In formal terms a function [Math Processing Error] is injective if [Math Processing Error] implies [Math Processing Error].

We also know that it's not surjective because no value maps to [Math Processing Error] (or any odd number) since if [Math Processing Error], then [Math Processing Error]. However, since [Math Processing Error], the function isn't surjective.

Answer is B.