### What does **inverse relation** mean?

# Definitions for inverse relation

in·verse re·la·tion

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **inverse relation**.

### Freebase

Inverse relation

In mathematics, the inverse relation of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'. In formal terms, if are sets and is a relation from X to Y then is the relation defined so that if and only if . In set-builder notation, . The notation comes by analogy with that for an inverse function. Although many functions do not have an inverse; every relation does have a unique inverse. Despite the notation and terminology, the inverse relation is not an inverse in the sense of group inverse; the unary operation that maps a relation to the inverse relation is however an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or more generally induces a dagger category on the category of relations as detailed below. As a unary operation, taking the inverse commutes however with the order-related operations of relation algebra, i.e. it commutes with union, intersection, complement etc.

### Numerology

Chaldean Numerology

The numerical value of inverse relation in Chaldean Numerology is:

**1**Pythagorean Numerology

The numerical value of inverse relation in Pythagorean Numerology is:

**6**

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"inverse relation." *Definitions.net.* STANDS4 LLC, 2023. Web. 30 May 2023. <https://www.definitions.net/definition/inverse+relation>.

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