Problem 2

Let f(x) = 3x/2. For this problem, we will use the notation cZ to denote the set of multiples of c.

For example, 2Z denotes the even integers, and 3Z denotes multiples of 3.

(a) Prove that f: 2Z → Z is not onto.

We discussed how to prove something is not onto in our second lecture on functions; you

should look there for reference to structure your proof.

Grading Notes. While a detailed rubric cannot be provided in advance as it gives away

solution details, the following is a general idea of how points are distributed for this problem.

We give partial credit where we can.

(3) Correctness. You must prove that f is not an onto function with the given domain and

codomain, with a convincing proof modelled on the similar proofs from our lectures.

(b) Prove that f: 2Z3Z is onto, where 3Z denotes the set of integers that are

multiples of 3.