Let $R\subseteq\mathbb{R}^2$. Consider the set of all "horizontal sections" $H_R =${$Rb|b\in\mathbb{R}$}, where $Rb=${$a\in\mathbb{R} | (a,b)\in R$}. Similarly consider the set of "vertical sections" of $R$, $V_R =${$ aR|a\in\mathbb{R}$} where $aR=${$ b\in\mathbb{R} | (a,b)\in R$}. Now define the equivalence relation on $\wp (\mathbb{R^2})$ such that $R \sim S$ if, and only if, $H_R=H_S$ and $V_R=V_S$.
QUESTION: What is the equivalence class of a disk?