Let $\mathbb{B} = \{ 0, 1 \}$ be the D217: Set of boolean numbers.
A D218: Boolean function $f : \mathbb{B} \times \mathbb{B} \to \mathbb{B}$ is a NAND boolean logic gate if and only if

(1)	\begin{equation} f(0, 0) = 1 \end{equation}
(2)	\begin{equation} f(1, 0) = 1 \end{equation}
(3)	\begin{equation} f(0, 1) = 1 \end{equation}
(4)	\begin{equation} f(1, 1) = 0 \end{equation}

A D218: Boolean function $f : \{ 0, 1 \} \times \{ 0, 1 \} \to \{ 0, 1 \}$ is a NAND boolean logic gate if and only if

(1)	\begin{equation} f(0, 0) = 1 \end{equation}
(2)	\begin{equation} f(1, 0) = 1 \end{equation}
(3)	\begin{equation} f(0, 1) = 1 \end{equation}
(4)	\begin{equation} f(1, 1) = 0 \end{equation}