negation (original) (raw)

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), P¯ (Hilbert) and N⁢P (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: ≠,⊈,∉,≇,∦,∤.