Negation
From Encyclopedia of Mathematics
The logical operation as a result of which, for a given statement 
, the statement "not A" is obtained. In formal languages, the statement obtained as result of the negation of a statement 
is denoted by 
, 
, 
, 
, 
(these are read: "not A" , "it is not true that A" , "A does not hold" , etc.). Semantically, the negation of a statement 
signifies that the assumption 
leads to a contradiction (cf. Contradiction (inconsistency)). In classical two-valued logic the following truth table applies for the operation of negation:'
, the statement "not A" is obtained. In formal languages, the statement obtained as result of the negation of a statement is denoted by , , , , (these are read: "not A" , "it is not true that A" , "A does not hold" , etc.). Semantically, the negation of a statement signifies that the assumption leads to a contradiction (cf. Contradiction (inconsistency)). In classical two-valued logic the following truth table applies for the operation of negation:'
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How to Cite This Entry:
Negation. V.E. Plisko (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Negation&oldid=18029
Negation. V.E. Plisko (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Negation&oldid=18029
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098