(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...
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?
Homework Statement
Definition: let R be an equivalence relation on a set X. A subset of X containing exactly one element from each equivalence class is called a complete set of representatives. now define a relation R on RxR by (x,y)R(u,v) <---> x^2 + y^2 = u^2 + v^2. You don't have to...
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...