Let $X$ be a D11: Set.
A D18: Map $f : Y \to Z$ is an enclosed binary operation on $X$ if and only if

(1)	$Y = X \times X$
(2)	$Z \subseteq X$

Let $X$ be a D11: Set.
A D554: Binary operation $f : X \times X \to Y$ on $X$ is enclosed if and only if $$\begin{equation} \forall \, x, y \in X : f(x, y) \in X \end{equation}$$

Let $X$ be a D11: Set.
A D554: Binary operation $f : X \times X \to Y$ on $X$ is enclosed if and only if $$\begin{equation} Y \subseteq X \end{equation}$$