2 a room in a hospital equipped for the performance of surgical operations; "great care is taken to keep the operating rooms aseptic" [syn: operating room, operating theater, operating theatre, surgery]
- Basque: edo, ala
- Bosnian: ili
- Breton: pe
- Catalan: o, o bé
- Chinese: 或 (huò); 或者 (huòzhě)
- Croatian: ili
- Czech: nebo
- Danish: eller
- Dutch: of
- Esperanto: aŭ
- Finnish: tai (exclusive, only in affirmative clauses); vai (inclusive, only in question clauses)
- French: ou
- German: oder
- Gothic: vau
- Greek: ή, είτε
- Hindi: या (yā)
- Hungarian: vagy
- Icelandic: eða
- Ido: od, o
- Indonesian: atau
- Interlingua: o
- Italian: o, od (euphonic alt. form used before a vowel), oppure
- Japanese: 又は (または, mata-wa), あるいは (arui-wa), か (ka)
- Korean: 또는 (ttoneun)
- Latin: aut (exclusive), vel (inclusive)
- Latvian: vai
- Maltese: jew
- Norwegian: eller
- Novial: o
- Old English: hwæþer þe, oþþe
- Persian: (yā)
- Polish: albo, lub, czy
- Portuguese: ou
- Romanian: ori, sau
- Russian: или (íli)
- Slovak: alebo, abo
- Slovene: ali
- Spanish: o, (before words beginning in 'o-' or 'ho-') u
- Swahili: au
- Swedish: eller
- Telugu: లేదా (léda)
- Turkish: veya
- Vietnamese: hay, hay là
Etymology 2aurum via or.
Alternative formsSometimes abbreviated as o. in heraldic contexts. Sometimes capitalized Or to distinguish use as a color from use as a conjunction.
gold or yellow tincture
- Of gold or yellow tincture on a coat of arms.
of yellow or gold tincture on a coat of arms
Etymology 2ha hora, alteration of hac hora.
EtymologyFrom ǫlr, órir
In logic and mathematics, or, also known as logical disjunction or inclusive disjunction is a logical operator that results in true whenever one or more of its operands are true. In grammar, or is a coordinating conjunction.
Logical disjunction is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false. More generally a disjunction is a logical formula that can have one or more literals separated only by ORs. A single literal is often considered to be a degenerate disjunction.
Truth tableThe truth table of p OR q (also written as p\orq (logic), p || q (in C-family languages in computer programming), or p + q (electronics)) is as follows:
Venn diagramThe Venn diagram of "p or q" (red is true)
The following properties apply to disjunction:
- associativity: a \lor (b \lor c) \equiv (a \lor b) \lor c
- commutativity: a \lor b \equiv b \lor a
- distributivity: (a \lor (b \land c)) \equiv ((a \lor b) \land (a \lor c))
- (a \land (b \lor c)) \equiv ((a \land b) \lor (a \land c))
- (a \lor (b \equiv c)) \equiv ((a \lor b) \equiv (a \lor c))
- (a \land (b \lor c)) \equiv ((a \land b) \lor (a \land c))
- idempotency: a \lor a \equiv a
- monotonicity: (a \rightarrow b) \rightarrow ((c \lor a) \rightarrow (c \lor b))
- (a \rightarrow b) \rightarrow ((a \lor c) \rightarrow (b \lor c))
- truth-preserving: The interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true' as a result of disjunction.
- falsehood-preserving: The interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false' as a result of disjunction.
The mathematical symbol for logical disjunction varies in the literature. In addition to the word "or", the symbol "\or", deriving from the Latin word vel for "or", is commonly used for disjunction. For example: "A \or B " is read as "A or B ". Such a disjunction is false if both A and B are false. In all other cases it is true.
All of the following are disjunctions:
- A \or B
- \neg A \or B
- A \or \neg B \or \neg C \or D \or \neg E
- \neg A \or B
The corresponding operation in set theory is the set-theoretic union.
Applications in computer scienceOperators corresponding to logical disjunction exist in most programming languages.
Bitwise operationDisjunction is often used for bitwise operations. Examples:
- 0 or 0 = 0
- 0 or 1 = 1
- 1 or 0 = 1
- 1 or 1 = 1
- 1010 or 1100 = 1110
The or operator can be used to set bits in a bitfield to 1, by or-ing the field with a constant field with the relevant bits set to 1.
Logical operationMany languages distinguish between bitwise and logical disjunction by providing two distinct operators; in languages following C, bitwise disjunction is performed with the single pipe (|) and logical disjunction with the double pipe (||) operators.
Logical disjunction is usually short-circuited; that is, if the first (left) operand evaluates to true then the second (right) operand is not evaluated. The logical disjunction operator thus usually constitutes a sequence point.
UnionThe union used in set theory is defined in terms of a logical disjunction: x ∈ A ∪ B if and only if (x ∈ A) ∨ (x ∈ B). Because of this, logical disjunction satisfies many of the same identities as set-theoretic union, such as associativity, commutativity, distributivity, and de Morgan's laws.
- Boole, closely following analogy with ordinary mathematics, premised, as a necessary condition to the definition of "x + y", that x and y were mutually exclusive. Jevons, and practically all mathematical logicians after him, advocated, on various grounds, the definition of "logical addition" in a form which does not necessitate mutual exclusiveness.
- Exclusive disjunction
- Affirming a disjunct
- Bitwise OR
- Boolean algebra (logic)
- Boolean algebra topics
- Boolean domain
- Boolean function
- Boolean-valued function
- Disjunctive syllogism
- Disjunction elimination
- Disjunction introduction
- First-order logic
- Logical graph
- Logical value
- OR gate
- Propositional calculus
or in Bulgarian: Логическа дизюнкция
or in Czech: Disjunkce
or in German: Disjunktion
or in Estonian: Disjunktsioon
or in Spanish: Disyunción lógica
or in Esperanto: Logika aŭo
or in French: Disjonction logique
or in Korean: 논리합
or in Indonesian: Logika disjungsi
or in Italian: Disgiunzione inclusiva
or in Hebrew: או (לוגיקה)
or in Lithuanian: Disjunkcija
or in Macedonian: Логичка дисјункција
or in Dutch: Logische disjunctie
or in Japanese: 論理和
or in Norwegian: Inklusiv disjunksjon
or in Polish: Alternatywa
or in Portuguese: Disjunção lógica
or in Simple English: Inclusive disjunction
or in Slovak: Disjunkcia (logika)
or in Serbian: Дисјункција
or in Swedish: Disjunktion (logik)
or in Thai: การเลือกเชิงตรรกศาสตร์
or in Ukrainian: Диз'юнкція (логічна)
achievement, alerion, and/or, animal charge, annulet, argent, armorial bearings, armory, arms, aureate, aureateness, auric, azure, bandeau, bar, bar sinister, baton, bearings, beige, bend, bend sinister, billet, blazon, blazonry, bordure, broad arrow, buff, buff-yellow, cadency mark, canary, canary-yellow, canton, chaplet, charge, chevron, chief, citron, citron-yellow, coat of arms, cockatrice, coronet, cream, creamy, crescent, crest, cross, cross moline, crown, device, difference, differencing, eagle, ecru, ermine, ermines, erminites, erminois, escutcheon, falcon, fallow, fallowness, fess, fess point, field, file, flanch, flaxen, fleur-de-lis, fret, fur, fusil, garland, gilded, gilt, gold, gold-colored, golden, griffin, gules, gyron, hatchment, helmet, heraldic device, honor point, impalement, impaling, inescutcheon, label, lemon, lemon-yellow, lion, lozenge, luteolous, lutescent, mantling, marshaling, martlet, mascle, metal, motto, mullet, nombril point, ocherish, ocherous, ochery, ochreous, ochroid, ochrous, ochry, octofoil, ordinary, orle, pale, paly, pean, pheon, primrose, primrose-colored, primrose-yellow, purpure, quarter, quartering, rose, sable, saffron, saffron-colored, saffron-yellow, sallow, saltire, sand-colored, sandy, scutcheon, shield, spread eagle, straw, straw-colored, subordinary, tenne, tincture, torse, tressure, unicorn, vair, vert, wreath, xanthic, xanthous, yale, yellow, yellowish, yellowishness, yellowness