Dictionary Definition
disjunctive adj : serving or tending to divide or
separate [ant: conjunctive]
User Contributed Dictionary
English
Adjective
Antonyms
conjunctiveExtensive 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
disjunctive in Bulgarian: Логическа
дизюнкция
disjunctive in Czech: Disjunkce
disjunctive in German: Disjunktion
disjunctive in Estonian: Disjunktsioon
disjunctive in Spanish: Disyunción lógica
disjunctive in Esperanto: Logika aŭo
disjunctive in French: Disjonction logique
disjunctive in Korean: 논리합
disjunctive in Indonesian: Logika
disjungsi
disjunctive in Italian: Disgiunzione
inclusiva
disjunctive in Hebrew: או (לוגיקה)
disjunctive in Lithuanian: Disjunkcija
disjunctive in Macedonian: Логичка
дисјункција
disjunctive in Dutch: Logische disjunctie
disjunctive in Japanese: 論理和
disjunctive in Norwegian: Inklusiv
disjunksjon
disjunctive in Polish: Alternatywa
disjunctive in Portuguese: Disjunção
lógica
disjunctive in Simple English: Inclusive
disjunction
disjunctive in Slovak: Disjunkcia (logika)
disjunctive in Serbian: Дисјункција
disjunctive in Swedish: Disjunktion
(logik)
disjunctive in Thai:
การเลือกเชิงตรรกศาสตร์
disjunctive in Ukrainian: Диз'юнкція
(логічна)
Synonyms, Antonyms and Related Words
ablative, adjectival, adjective, adverb, adverbial, adversative
conjunction, alternative, attributive, biodegradable, broken, broken off, choppedoff,
choppy, conjunction, conjunctive
adverb, coordinating conjunction, copulative, copulative
conjunction, correlative conjunction, corrosive, decomposable, decomposing, decousu, degradable, dilapidated, disconnected, discontinued, discontinuous, discrete, discretional, disintegrable, disintegrated, disintegrating, disintegrative,
disjunctive conjunction, disruptive, dividing, elective, episodic, erosive, exclamatory noun,
fitful, form class, form
word, function class, gerundive, herkyjerky,
incoherent, interjection, intermittent, interrupted, irregular, jagged, jerky, moldering, noncontinuous, nonlinear, nonsequential, nonserial, nonuniform, optional, parenthetic, part of speech,
participle, particle, parting, past participle,
patchy, perfect
participle, preposition, present
participle, ravaged,
resolvent, ruinous, scrappy, separating, separative, snatchy, solvent, spasmodic, spotty, subordinating
conjunction, suspended, unconnected, unjoined, unsuccessive, verbal
adjective, volitional, voluntary, worn