Problem 1

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: Z→ Z is not a function (that is, it is not a function if both its domain

and codomain are integers.)

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 a function with a convincing proof modelled

on the similar proofs from our lectures.

(b) Prove that f: 2Z → Z is a function (that is, it is a function if its domain is even

integers and its codomain is all integers.)