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# logical negation symbol

The logical negation symbol is used in Boolean algebra to indicate that the truth value of the statement that follows is reversed. The symbol resembles a dash with a 'tail' (¬). The arithmetic subtraction symbol (-) or tilde (~) are also used to indicate logical negation.

The simplest use of a negation symbol is with a single sentence. For example, if A represents the statement "The sky is blue," then ¬A represents the statement "The sky is not blue" or "It is not true that the sky is blue."

The negation symbol is often found within, or preceding, complex logical statements. In Boolean algebra, the plus sign (+) represents the logical inclusive OR, and the asterisk (*) represents the logical AND. Rules for use of the logical negation symbol become more complicated when the symbol appears in complex statements. For example, these pairs of statements are not equivalent for all A and for all B:

¬(A + B)
(¬A) + (¬B)

¬(A * B)
(¬A) * (¬B)

However, 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 Boolean algebra, and the Mathematical Symbols .

This was last updated in September 2005

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