**canonical empty binary relation**if and only if

(1) | $R = \emptyset$ | D857: Empty binary relation |

(2) | $X \times Y = \emptyset$ |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Empty binary relation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Empty binary relation

Formulation 0

A D4: Binary relation $(X \times Y, R)$ is a **canonical empty binary relation** if and only if

(1) | $R = \emptyset$ | D857: Empty binary relation |

(2) | $X \times Y = \emptyset$ |