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Definition

logical AND symbol

For a practical application, see logic gate .

The logical AND symbol is used in Boolean algebra to indicate a conjunction between two statements. A conjunction is true if, but only if, both of its components are true. The most commonly used symbol is an asterisk (*).

The simplest use of the AND symbol is with a sentence consisting of two statements. For example, if A represents the statement 'It is cold' and B represents the statement 'It is rainy', then A * B represents the statement 'It is cold and rainy.'

The AND 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 OR operation is represented by a plus sign (+). 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 .

This was last updated in September 2005
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