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Negation

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The logical operation as a result of which, for a given statement $A$, the statement "not A" is obtained. In formal languages, the statement obtained as result of the negation of a statement $A$ is denoted by $\neg A$, $\sim A$, $\overline A$, $-A$, $A'$ (these are read: "not A", "it is not true that A", "A does not hold", etc.). Semantically, the negation of a statement $A$ signifies that the assumption $A$ leads to a contradiction (cf. Contradiction (inconsistency)). In classical two-valued logic the following truth table applies for the operation of negation:

$A$ $\neg A$
$T$ $F$
$F$ $T$
How to Cite This Entry:
Negation. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Negation&oldid=32853
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article