Let $X$ and $Y$ each be a D17: Finite set such that

(i) | $N, M \in \mathbb{N}$ are each a D996: Natural number |

(ii) | \begin{equation} |X| = N, \quad |Y| = M \end{equation} |

(iii) | $X \times Y$ is the D191: Binary cartesian set product of $X$ and $Y$ |

(iv) | $\mathcal{B} : = \{ R : R \subseteq X \times Y \}$ is the D5348: Set of binary relations on $X \times Y$ |

Then
\begin{equation}
|\mathcal{B}|
= 2^{N M}
\end{equation}