|
In logic and mathematics, logical disjunction (written or) is a logical operator that results in true just whenever some of its operands are true.
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. The truth table of p OR q (also written as p ∨ q) is as follows: 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. Symbol The mathematical symbol for logical disjunction varies in the literature. In addition to the word "or", the symbol "∨", deriving from the Latin word vel for "or", is commonly used for disjunction. For example: "A ∨ 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 ∨ B ¬A ∨ B A ∨ ¬B ∨ ¬C ∨ D ∨ ¬E The corresponding operation in set theory is the set-theoretic union. Associativity and commutativity For more than two inputs, or can be applied to the first two inputs, and then the result can be or'ed with each subsequent input: (A or (B or C)) ⇔ ((A or B) or C) Because or is associative, the order of the inputs does not matter: the same result will be obtained regardless of association. The operator xor is also commutative and therefore the order of the operands is not important: A or B ⇔ B or A Bitwise operation Disjunction is often used for bitwise operations. Examples: Note that in computer science the OR operator can be used to set a bit to 1 by OR-ing the bit with 1. 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 set-theoretic union, such as associativity, commutativity, distributivity, and de Morgan's laws. Notes Logical operators Related topics | ||||||||
|
| |||||||||
 |
|
| |