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!