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## relation

relation (defined on sets S1, S2,… Sn) A subset R of the Cartesian product S1 × S2 × … × Sn

of the n sets S1, …, Sn. This is called an n-ary relation. When a relation R is defined on a single set S the implication is that R is a subset of S × S × … × S (n terms)

The most common situation occurs when n = 2, i.e. R is a subset of S1 × S2. Then R is called a binary relation on S1 to S2 or between S1 and S2. S1 is the domain of R and S2 the codomain of R. If the ordered pair (s1,s2) belongs to the subset R, a notation such as s1 R s2 or s1 ρ s2

is usually adopted and it is then possible to talk about the relation R or ρ and to say that s1 and s2 are related.

An example of a binary relation is the usual “is less than” relation defined on integers, where the subset R consists of ordered pairs such as (4,5); it is however more natural to write 4 < 5. Other examples include: “is equal to” defined on strings, say; “is the square root of” defined on the nonnegative reals; “is defined in terms of” defined on the set of subroutines within a particular program; “is before in the queue” defined on the set of jobs awaiting execution at a particular time.

The function is a special kind of relation. Graphs are often used to provide a convenient pictorial representation of a relation.

Relations play an important part in theoretical aspects of many areas of computing, including the mathematical foundations of the subject, databases, compiling techniques, and operating systems. See also equivalence relation, partial ordering.

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## relation

re·la·tion / riˈlāshən/ • n. 1. the way in which two or more concepts, objects, or people are connected; a thing's effect on or relevance to another: questions about the relation between writing and reality the size of the targets bore no relation to their importance. ∎  (relations) the way in which two or more people, countries, or organizations feel about and behave toward each other: the improvement in relations between the two countries the meetings helped cement Anglo-American relations. ∎  (relations) chiefly formal sexual intercourse: he wanted an excuse to abandon sexual relations with her. 2. a person who is connected by blood or marriage; a kinsman or kinswoman: she was no relation at all, but he called her Aunt Nora. 3. the action of telling a story. PHRASES: in relation to in the context of; in connection with: there is an ambiguity in the provisions in relation to children's hearings.

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"relation." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 12 Dec. 2017 <http://www.encyclopedia.com>.

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# RELATION

Kin; relative. The connection of two individuals, or their situation with respect to each other, who are associated, either by law, agreement, or kinship in a social status or union for purposes of domestic life, such asparent and childorhusband and wife.

The doctrine of relation is the principle by which an act performed at one time is deemed, through a legal fiction, to have been performed at a prior time. For example, in the conveyance of real property, the final proceeding that completes the transfer of property is considered, for certain purposes, to have become effective by relation as of the day when the first proceeding took place. Relation, in essence, is the legal term for retroactive effect.

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## relation

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natation, nation, negation, notation, nutation, oblation, oration, ovation, potation, relation, rogation, rotation, Sarmatian, sedation, Serbo-Croatian, station, taxation, Thracian, vacation, vexation, vocation, zonation •accretion, Capetian, completion, concretion, deletion, depletion, Diocletian, excretion, Grecian, Helvetian, repletion, Rhodesian, secretion, suppletion, Tahitian, venetian •academician, addition, aesthetician (US esthetician), ambition, audition, beautician, clinician, coition, cosmetician, diagnostician, dialectician, dietitian, Domitian, edition, electrician, emission, fission, fruition, Hermitian, ignition, linguistician, logician, magician, mathematician, Mauritian, mechanician, metaphysician, mission, monition, mortician, munition, musician, obstetrician, omission, optician, paediatrician (US pediatrician), patrician, petition, Phoenician, physician, politician, position, rhetorician, sedition, statistician, suspicion, tactician, technician, theoretician, 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electrocution, elocution, evolution, execution, institution, interlocution, irresolution, Lilliputian, locution, perlocution, persecution, pollution, prosecution, prostitution, restitution, retribution, Rosicrucian, solution, substitution, volution •cushion • resumption • München •pincushion •Belorussian, Prussian, Russian •abduction, conduction, construction, deduction, destruction, eduction, effluxion, induction, instruction, introduction, misconstruction, obstruction, production, reduction, ruction, seduction, suction, underproduction •avulsion, compulsion, convulsion, emulsion, expulsion, impulsion, propulsion, repulsion, revulsion •assumption, consumption, gumption, presumption •luncheon, scuncheon, truncheon •compunction, conjunction, dysfunction, expunction, function, junction, malfunction, multifunction, unction •abruption, corruption, disruption, eruption, interruption •T-junction • liposuction •animadversion, aspersion, assertion, aversion, Cistercian, coercion, conversion, desertion, disconcertion, dispersion, diversion, emersion, excursion, exertion, extroversion, immersion, incursion, insertion, interspersion, introversion, Persian, perversion, submersion, subversion, tertian, version •excerption