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