Negation

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition ${\displaystyle P}$ to another proposition "not ${\displaystyle P}$", standing for "${\displaystyle P}$ is not true", written ${\displaystyle \neg P}$, ${\displaystyle {\mathord {\sim }}P}$ or ${\displaystyle {\overline {P}}}$. It is interpreted intuitively as being true when ${\displaystyle P}$ is false, and false when ${\displaystyle P}$ is true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity (and vice versa). In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition ${\displaystyle P}$ is the proposition whose proofs are the refutations of ${\displaystyle P}$.

Negation

NOT
Definition	${\displaystyle \lnot {x}}$
Truth table	${\displaystyle (01)}$
Logic gate
Normal forms
Disjunctive	${\displaystyle \lnot {x}}$
Conjunctive	${\displaystyle \lnot {x}}$
Zhegalkin polynomial	${\displaystyle 1\oplus x}$
Post's lattices
0-preserving	no
1-preserving	no
Monotone	no
Affine	yes