# Discrete Mathematics help

## Homework Statement

Find the range of the function g: ZxZ --> ZxZ given by g(m,n)=(m-n,m+n). Hints: First recall that if f: A ---> B then Range (f)={b e B such that there exists an A in A with b=f(a). Second, if you claim that some set C is the range, then you must show that i) C is a subset Range(f) and ii) range (f) is a subset of C. Both i and ii are required to conclude that C=range(f).

none

## The Attempt at a Solution

I am think that the range is all integers from -infinity to +infinity.

I know that:
* ZxZ denotes a set of ordered pairs.
* m,n exist in Z
* range (g) exists in Z

I don't know where to go with this!

## The Attempt at a Solution

Dick
Homework Helper
The range is all pairs (p,q) such that (p,q)=(m+n,m-n) for integers m and n. Solve for m and n in terms of p and q. Now rethink your guess that the range is all integer pairs. E.g. is (1,2) in the range?

So we figured out that p=q. So our new guess for the range is all integers such that p=q for the ordered pair (p,q). If we say that, is that enough to justify our answer?

Dick
Homework Helper
How did you figure out p=q? p=m+n, q=m-n for the domain value (m,n) and ask yourself when m and n are both integers. That's two equations in two unknowns. Solve them. Your new guess is worse than the last.

Dick
Homework Helper
Actually, let's go back. You never answered my question. Is (1,2) in the range? If you answer that it will give you a big clue in a non-abstract sense.

(1,2) is not in the range. When substituted in the equations for p and q the results for m and n are not integers.
After looking at your first response to our terrible answer, we looked that problem and decided that the range is (p,q) when p and q are any even integers.
**I am working on this a group of people and the more we talk about it, the more confused we get.**

Dick