negation
In logics and mathematics, negation (from Latin negare ‘to deny’) is the unary operation “¬” which swaps the truth value of any operand to the truth value. So, if the statement P is true then its negated statement ¬P is false, and vice versa.
Note 1. The negated statement ¬P (by Heyting) has been denoted also with -P (Peano), ∼P (Russell), ˉP (Hilbert) and NP (by the Polish notation).
Note 3. The negation of logical or and logical and give the results
Analogical results concern the quantifier statements:
These all are known as de Morgan’s laws.
Note 4. Many mathematical relation statements, expressed with such special relation symbols as , are negated by using in the symbol an additional cross line:
.
Title | negation |
---|---|
Canonical name | Negation |
Date of creation | 2015-04-25 17:44:13 |
Last modified on | 2015-04-25 17:44:13 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 03B05 |
Synonym | logical not |
Related topic | SetMembership |