Negation
From Encyclopedia of Mathematics - Reading time: 1 min
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) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Negation9 views | Status: cached on June 27 2024 00:22:53↧ Download this article as ZWI file
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