1. The problem statement, all variables and given/known data Let X be Z*Z, i.e. X is the set of all ordered pairs of the form (x; y) with (x, y) are integers. Define the relation R on X as follows: (x1^2, x2^2)R(y1^2, y2^2) = (x1^2 + x2^2) = (y1^2 + y2^2) 2. Relevant equations By definition, an equivalence relation bears the following characteristics, reflexive, transitive symmetric Further information here, http://www.math.csusb.edu/notes/rel/node3.html 3. The attempt at a solution Not an equivalence relation? Although it is reflective, the transitive and symmetric characteristics don't hold because if per say, we have x1 = 1, x2 = 2, y1 = 3, y2 = 4, the relation doesn't hold to start with... Is this a strong explanation? Or better suggestions? I feel that it's more complicated than this?