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logical disjunction : ウィキペディア英語版
logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the ''or'' of a set of operands is true if and only if ''one or more'' of its operands is true. The logical connective that represents this operator is typically written as ∨ or +.
"''A'' or ''B''" is true if ''A'' is true, or if ''B'' is true, or if both ''A'' and ''B'' are true.
In logic, ''or'' by itself means the ''inclusive'' ''or'', distinguished from an exclusive or, which is false when both of its arguments are true, while an "or" is true in that case.
An operand of a disjunction is called a disjunct.
Related concepts in other fields are:
* In natural language, the coordinating conjunction "or".
* In programming languages, the short-circuit or control structure.
* In set theory, union.
* In predicate logic, existential quantification.
==Notation==

Or is usually expressed with an infix operator: in mathematics and logic, ∨; in electronics, +; and in most programming languages, |, ||, or or. In Jan Łukasiewicz's prefix notation for logic, the operator is A, for Polish ''alternatywa''.〔Józef Maria Bocheński (1959), ''A Précis of Mathematical Logic'', translated by Otto Bird from the French and German editions, Dordrecht, North Holland: D. Reidel, passim.〕

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