Let $X$ be a D17: Finite set such that

(i)	$K : = |X| \in \mathbb{N} = \{ 0, 1, 2, 3, \ldots \}$
(ii)	$X^N = \prod_{n = 1}^N X$ is a D326: Cartesian product
(iii)	$\mathcal{R} : = \{ R : R \subseteq X^N \}$ is a D5494: Set of N-ary relations on $X^N$

Then \begin{equation} |\mathcal{R}| = 2^{K^N} \end{equation}

Let $X$ be a D17: Finite set such that

(i)	$K : = |X| \in \mathbb{N} = \{ 0, 1, 2, 3, \ldots \}$
(ii)	$X^N = \prod_{n = 1}^N X$ is a D326: Cartesian product
(iii)	$\mathcal{R} : = \{ R : R \subseteq X^N \}$ is a D5494: Set of N-ary relations on $X^N$

Then \begin{equation} |\mathcal{R}| = 2^{\underbrace{K K \cdots K}_{N \text{ times}}} \end{equation}