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

**set of binary relations**on $X \times Y$ is the D11: Set \begin{equation} \{ R : R \subseteq X \times Y \} \end{equation}

▼ | Set of symbols |

▼ | Alphabet |

▼ | Deduction system |

▼ | Theory |

▼ | Zermelo-Fraenkel set theory |

▼ | Set |

▼ | Binary cartesian set product |

▼ | Binary relation |

Definition D5348

Set of binary relations

Formulation 0

Let $X$ and $Y$ each be a D11: Set such that

The **set of binary relations** on $X \times Y$ is the D11: Set
\begin{equation}
\{ R : R \subseteq X \times Y \}
\end{equation}

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

Results

▶ | Number of binary relations on a finite set |

▶ | Number of binary relations on binary cartesian product |