Dictionary Definition
disjunction
Noun
2 the act of breaking a connection [syn: disconnection]
User Contributed Dictionary
Noun
disjunction (plural disjunctions) The proposition resulting from the combination of two or more propositions using the or operator.
 a logical operator that results in true when some of its operands are true.
 During meiosis, the seperation of chromosomes (homologous in meiosis I, and sister chromotids in meiosis II).
Translations
logic
 Czech: disjunkce
 French: disjonction
 German: Disjunktion
 Portuguese: disjunção
See also
References
 "Disjunction" in the Stanford Encyclopedia of Philosophy
 "Disjunction" in Wolfram MathWorld
Extensive Definition
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.
Definition
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 table
The truth table of p OR q (also written as p\orq (logic), p  q (in Cfamily languages in computer programming), or p + q (electronics)) is as follows:Venn diagram
The Venn diagram of "p or q" (red is true)Properties
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))

 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))

 truthpreserving: The interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true' as a result of disjunction.
 falsehoodpreserving: The interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false' as a result of disjunction.
Symbol
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
The corresponding operation in set theory is the
settheoretic
union.
Applications in computer science
Operators corresponding to logical disjunction exist in most programming languages.Bitwise operation
Disjunction 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
oring the field with a constant field with the relevant bits set
to 1.
Logical operation
Many 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 shortcircuited;
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.
Although in most languages the type of a logical
disjunction expression is boolean and thus can only have the value
true or false, in some (such as
Python and JavaScript) the
logical disjunction operator returns one of its operands; the first
operand if it evaluates to a true value, and the second operand
otherwise.
Union
The 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 settheoretic union, such as associativity, commutativity, distributivity, and de Morgan's laws.Notes
 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.
See also
 Exclusive disjunction
 Affirming a disjunct
 Bitwise OR
 Boolean algebra (logic)
 Boolean algebra topics
 Boolean domain
 Boolean function
 Booleanvalued function
 Disjunctive syllogism
 Disjunction elimination
 Disjunction introduction
 Firstorder logic
 Logical graph
 Logical value
 Operation
 Operator
 OR gate
 Propositional calculus
External links
disjunction in Bulgarian: Логическа
дизюнкция
disjunction in Czech: Disjunkce
disjunction in German: Disjunktion
disjunction in Estonian: Disjunktsioon
disjunction in Spanish: Disyunción lógica
disjunction in Esperanto: Logika aŭo
disjunction in French: Disjonction logique
disjunction in Korean: 논리합
disjunction in Indonesian: Logika
disjungsi
disjunction in Italian: Disgiunzione
inclusiva
disjunction in Hebrew: או (לוגיקה)
disjunction in Lithuanian: Disjunkcija
disjunction in Macedonian: Логичка
дисјункција
disjunction in Dutch: Logische disjunctie
disjunction in Japanese: 論理和
disjunction in Norwegian: Inklusiv
disjunksjon
disjunction in Polish: Alternatywa
disjunction in Portuguese: Disjunção
lógica
disjunction in Simple English: Inclusive
disjunction
disjunction in Slovak: Disjunkcia (logika)
disjunction in Serbian: Дисјункција
disjunction in Swedish: Disjunktion
(logik)
disjunction in Thai:
การเลือกเชิงตรรกศาสตร์
disjunction in Ukrainian: Диз'юнкція
(логічна)
Synonyms, Antonyms and Related Words
ablation, abstraction, accord, addition, adjunct, affairs, affiliation, affinity, alienation, alliance, aloofness, alteration, analysis, anarchy, anatomization, approximation, assemblage, association, atomization, bond, breakup, broken thread, brokenness, change, chaos, clearance, closeness, combination, confusion, connectedness, connection, contiguity, contrariety, corrosion, crumbling, dealings, decay, decomposition, deduction, degradation, demarcation, deportation, derangement, desynonymization,
detachment, differencing, differentiation,
diffusion, dilapidation, disarrangement, disarray, disarticulation,
disassociation,
discard, discomfiture, discomposure, disconcertedness,
disconnectedness,
disconnection,
discontinuance,
discontinuation,
discontinuity,
discontinuousness,
discreteness,
discrimination,
disengagement,
disequalization,
disharmony, dishevelment, disintegration, disjointing, disjuncture, dislocation, disorder, disorderliness, disorganization,
dispersal, dispersion, disposal, disposition, disproportion, disruption, dissociation, dissolution, distinction, distinguishment,
disturbance,
disunion, diversification,
division, divorce, divorcement, ejection, elimination, entropy, episode, eradication, erosion, exile, expatriation, expulsion, filiation, fitfulness, haphazardness, homology, immateriality, impertinence, inapplicability,
inappositeness,
incoherence,
incompleteness,
inconnection,
inconsequence,
inconsistency,
independence,
indiscriminateness,
individualization,
individuation,
inharmonious harmony, intercourse, intermittence, intimacy, irregularity, irrelation, irrelevance, isolation, junction, liaison, link, linkage, linking, liquidation, luxation, modification, most admired
disorder, mutual attraction, nearness, non sequitur,
nonadhesion,
noncohesion,
noncontinuance,
nonlinearity,
nonseriality,
nonsymmetry,
nonuniformity,
ostracism, outlawing, outlawry, parenthesis, particularization,
parting, partition, personalization,
perturbation,
promiscuity,
promiscuousness,
propinquity,
proximity, purge, randomness, rapport, ravages of time,
relatedness,
relation, relations, relationship, removal, resolution, riddance, scattering, segmentation, segregation, separateness, separation, separatism, severalization, severance, similarity, specialization, subdivision, subtraction, suspension, sympathy, tie, tiein, turbulence, unadherence, unadhesiveness, unconnectedness,
union, unrelatedness, unsymmetry, untenacity, ununiformity, upset, variation, wear, wear and tear, withdrawal, zoning