Equivalence Relations and Classes 3 I am studying for a discrete math exam that is tomorrow and the questions on equivalence classes are not making sense to me.
Practice Problem: Let $\sim$ be the relation defined on set of pairs $(x, y) \in R^2$ such that $(x, y) \sim (p, q)$ if and only if $x^2 + y^2 = p^2 + q^2$. Find three elements in the equivalence class $[(0, 1)]$
The example solution shows $(0,1),(1,0),(-1,0),$ can somebody explain why those solutions hold true for this equivalence class? Thank you!

The equivalence relation is defined such that $(x,y) \sim (p,q)$ if $x^2 + y^2 = p^2 + q^2$.
If $(x,y) \in[(0,1)]$, then $(x,y) \sim (0,1)$, so it must satisfy
$$
x^2 + y^2 = 0^2 + 1^2 = 1
$$
Which is the equation of the unit circle, which all three of those points are a part of.
