Hello, I was given a problem and I listed it below. I have finished everything up to the finding the equivalence class.

Let f be any function from A × A to A. (That is, f is a function of two variables

defined on the entire plane.) Define a relation Af by the rule: (x,y) Af (z,w) if and only if f(x,y)

= f(z,w). Show that Af is an equivalence relation. (Hint: first consider a simple specific case,

such as f(x) = x^2 + y^2.)

For the special case f(x) = x^2 + y^2 in the previous problem, what are the equivalence classes?

I have completed proving why the question is reflexive, symmetric, and transitive, but I do not understand how I am supposed to determine what the equivalence classes are since there are no numbers involved. What I have at the moment is [x] = {(x, y)| x belongs to A and y belongs to A}, but I'm not sure if that is correct. If anyone could give me advice or some type of reference to follow it would be greatly appreciated!