**binary relation structure**if and only if

(1) | $X \times Y$ is a D326: Cartesian product |

(2) | $R$ is a D4: Binary relation on $X \times Y$ |

▼ | Set of symbols |

▼ | Alphabet |

▼ | Deduction system |

▼ | Theory |

▼ | Zermelo-Fraenkel set theory |

▼ | Set |

▼ | Binary cartesian set product |

▼ | Binary relation |

Definition D1104

Binary relation structure

Formulation 0

An D548: Ordered pair $(X \times Y, R)$ is a **binary relation structure** if and only if

(1) | $X \times Y$ is a D326: Cartesian product |

(2) | $R$ is a D4: Binary relation on $X \times Y$ |