Give on the set $A$ to the equivalence $\rho$ ,classes $ A = \mathbb{Z}, \rho = \{(x,y): xy > 0$ or $ x = y= 0\}$

Question

$ A = \mathbb{Z}, \rho = \{(x,y): xy > 0$or $ x = y= 0\}$

I assume that one class should be if non of $x$ or $y$ are equal to zero and in this case I would get the positive part of the Descartes coordinate system, I mean where $x$ and $y$ are both positive, so I would get the positive coordinates of the grid.

And the other class will be the negative part of the $x$ and $y$ axis.

So I would get 2 classes in this case, is my solution correct?

Answer 1

What about $x=y=0$? Doesn't that make $3$ classes? I count $3$... the two you mentioned, and this one...