relation
Pluralrelations
- 1The manner and tone in which people, groups, or states interact and deal with one another.
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.
UsageUsually relations between two sides or relations with one, often after a field: foreign relations, labor relations.
- 2The way in which two things are connected or associated with 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.
Usagethe relation between A and B; set phrases bear little relation to something and in relation to something.
Similarconnection, link, association, correlation
- 3A member of one's extended family; a relative by blood or marriage.
He inherited the farm from a relation on his mother's side.
She spent the holidays visiting relations she hadn't seen in years.
UsageOften a distant relation or a relation on one's mother's side; relative means the same.
- 4Sexual intercourse; used especially in formal or legal contexts, often in the phrase sexual relations.
He denied under oath that he had had relations with the witness.
Canon law treated any carnal relation outside marriage as grounds for penance.
UsageUsually sexual relations; a bare have relations with someone is read this way, so add good or diplomatic for dealings.
Similarintercourse, sex
- 5In mathematics, a set of ordered pairs, or more generally of ordered tuples, that specifies which elements of given sets are related to one another.
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.
Note
The workhorse case is a subset of the product of two sets, where order matters, so (2, 5) can belong while (5, 2) does not. Most named properties are defined for it. A relation may be symmetric, as equality is, or fail to be, as divisibility does. Orderings, equivalence relations and even functions are all binary relations with extra conditions.
Checked 6 Nov 2026 · 7 facts
- A binary relation is a subset of a Cartesian product of two sets; reversing an ordered pair need not preserve membership. math.hkust.edu.hk
- The standard named relation properties are defined for binary relations. faculty.washington.edu
- Equality is symmetric. cs.cornell.edu
- Divisibility is not symmetric on the integers. math.cmu.edu
- Orderings are binary relations satisfying additional conditions. www3.risc.jku.at
- Equivalence relations are binary relations satisfying reflexivity, symmetry and transitivity. math.ucla.edu
- Functions are binary relations with exactly one output for each input. mathresearch.utsa.edu
Less common meanings
- 6The act of telling or recounting a story or series of 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.
UsageUsually a relation of events, in careful prose; account is the everyday word.
Similaraccount, narration, narrative, report, telling
Note
The noun that belongs to the verb relate, "to tell," and a reminder that the Latin root meant carrying something back. John Skelton's Ware the Hauke, written in the early 1500s, promises "I shall you make relacyon," with make relation meaning to give an account.
- 7A set of tuples, implemented as a table in a relational database, with each tuple forming one row.
The orders relation stores one tuple for every purchase made through the site.
Normalizing the schema split the original relation into three smaller ones.
Similartable
Note
Database theory took the set-theory notion directly. The relational in relational database refers to this, a table understood as a set of tuples, and not to links between tables. Each row is a tuple and each column a named attribute. Because it is a set, it has no inherent row order and no duplicate rows. A key, such as a customer's ID number, picks out one tuple uniquely.
Checked 6 Nov 2026 · 5 facts
- The relational database model adopted mathematical relations; its name refers to relations as sets of tuples, rather than links between tables. web.eecs.umich.edu
- Rows correspond to tuples and columns to named attributes. alg.manifoldapp.org
- A relation has no inherent row order. web.eecs.umich.edu
- A relation has no duplicate rows. web.eecs.umich.edu
- A key uniquely identifies a tuple; an assigned customer ID can serve as one. runestone.academy
- 8In group theory, an equation stating that two products of a group's generators are equal, used in the presentation of the group.
- 9In category theory, a subobject of a product of objects, generalizing the idea of a set of ordered tuples.
Practice
Can you tell the meanings of relation apart? Answer 3 quick questions from this page, or write your own sentence and AI will check it.
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").
Checked 6 Nov 2026 · 7 facts
- English relation derives from Middle English relacion through Anglo-Norman and Old French, ultimately from Latin relātiō. en.wiktionary.org
- Latin relātiō is a noun formed from the stem of relātus. en.wiktionary.org
- Relātus is the past participle of referō. en.wiktionary.org
- Referō means “I refer, I relate.” en.wiktionary.org
- Referō combines re- and ferō. en.wiktionary.org
- Latin re- means “again.” en.wiktionary.org
- Latin ferō means “I bear, I carry.” en.wiktionary.org