# relation

Pronunciation: say "ri-LAY-shuhn" /ɹɪˈleɪʃən/

## Noun

1. The manner and tone in which people, groups, or states interact and deal with one another.
   - Simple: The way people, groups, or countries get along and deal with each other.
   - _Trade talks stalled, and relations between the two countries grew tense through the winter._
   - _Labor relations at the plant have been tense since the layoffs began._
2. The way in which two things are connected or associated with each other.
   - Simple: A connection or link between two things, or the way they affect each other.
   - _The study examined the relation between interest rates and housing prices._
   - _Her salary bears little relation to the amount of work she does._
3. A member of one's extended family; a relative by blood or marriage.
   - Simple: A person who is part of your family, like a cousin, aunt, or uncle.
   - _He inherited the farm from a relation on his mother's side._
   - _She spent the holidays visiting relations she hadn't seen in years._
4. Sexual intercourse; used especially in formal or legal contexts, often in the phrase sexual relations.
   - Simple: A polite, formal word for the act of sex.
   - _He denied under oath that he had had relations with the witness._
   - _Canon law treated any carnal relation outside marriage as grounds for penance._
6. The act of telling or recounting a story or series of events.
   - Simple: The act of telling a story or describing events.
   - _The witness's relation of the night's events matched the physical evidence._
   - _Travel books of that era often opened with a relation of the voyage out._
5. In mathematics, a set of ordered pairs, or more generally of ordered tuples, that specifies which elements of given sets are related to one another.
   - Simple: In math, a set of pairs (or longer ordered lists) of things that shows which ones are linked.
   - _The relation 'less than' on the integers contains the pair (2, 5) but not (5, 2)._
   - _Equality is a relation that pairs every number with itself._
7. A set of tuples, implemented as a table in a relational database, with each tuple forming one row.
   - Simple: In a database, a table that stores information in rows and columns.
   - _The orders relation stores one tuple for every purchase made through the site._
   - _Normalizing the schema split the original relation into three smaller ones._

## Other meanings

- (noun) In group theory, an equation stating that two products of a group's generators are equal, used in the presentation of the group.
- (noun) In category theory, a subobject of a product of objects, generalizing the idea of a set of ordered tuples.

## Origin

From Middle English relacion, borrowed via Anglo-Norman and Old French relacion from Latin relātiō, a noun formed from relātus, the past participle of the verb referō ("I refer, I relate"). That verb combines the prefix re- ("again") with ferō ("I bear, I carry").

Source: DictionaryAI, https://dictionaryai.com/define/relation (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).