logical OR symbol

For a practical application, see logic gate .

The logical OR symbol is used in Boolean algebra to indicate an inclusive disjunction between two statements. An inclusive disjunction is true if either, or both, of its components are true. The most commonly used symbol is a plus sign (+).

The simplest use of the OR symbol is with a sentence consisting of two statements. For example, if A represents the statement 'It is raining' and B represents the statement 'It is snowing', then A + B represents the statement 'It is raining or snowing, or both.'

The OR symbol is often found within complex logical statements along with other symbols. In Boolean algebra, negation (also called the NOT operation) is represented by a dash with a 'tail' (¬). The logical AND operation is represented by an asterisk (*). Certain facts involving negation, the OR operation, and the AND operation have been proven in Boolean algebra, and are known as DeMorgan's Laws. According to these theorems, the following pairs of statements are logically equivalent for all A and for all B:

¬(A + B)
(¬A) * (¬B)

¬(A * B)
(¬A) + (¬B)

Also see Mathematical Symbols .