Let $\mathbb{B} = \{ 0, 1 \}$ be the D217: Set of boolean numbers.
A D18: Map $f : X \to Y$ is a boolean logic gate if and only if

(1)	\begin{equation} \exists \, N \in 1, 2, 3, \ldots : X = \mathbb{B}^N \end{equation}
(2)	\begin{equation} Y = \mathbb{B} \end{equation}

A D18: Map $f : X \to Y$ is a boolean logic gate if and only if

(1)	\begin{equation} \exists \, N \in 1, 2, 3, \ldots : X = \{ 0, 1 \}^N \end{equation}
(2)	\begin{equation} Y = \{ 0, 1 \} \end{equation}