For what $A,B \subset \mathbb R$ is $\{(x,y) \in A \times B \mid x^2-y^2=0\}$ a well defined bijection? For what $A,B \subset \mathbb R$ is relation $\{(x,y) \in A \times B \mid x^2-y^2=0\}$ a well defined bijection from $A$ to $B$?
This concept is pretty new for me so I'm not sure how to show this on the right way.

As it stands $x^2 - y^2 = 0$
$x = y$ or $x = -y$
So, how do we restrict $A$ and $B$ so that only one of the above holds?
Restrict $A$ to either the positive reals or the negative reals, and $B$ to either the positive reals or the negative reals.
And then for every $x\in A$ there will be a unique $y\in B$ that satisfies the relation.  And for every $y \in B$ there is one $x\in A$  
