A D11: Set $X $ is a transitive set if and only if \begin{equation} \forall \, x \in X : \forall \, y \in x : y \in X \end{equation}

A D11: Set $X $ is a transitive set if and only if \begin{equation} \forall \, x \in X : x \subseteq X \end{equation}

A D11: Set $X $ is a transitive set if and only if \begin{equation} X \subseteq \mathcal{P}(X) \end{equation}