Negáció

Negáció, or negation, is the operation that inverts the truth value of a proposition. If P is true, the negation ¬P is false, and if P is false, ¬P is true. In natural language, negation expresses denial or contradiction; in formal systems, it is a precise logical operator.

Formally, negation is a unary operator applied to a statement or predicate. In classical propositional logic, ¬¬P is equivalent to P, while in intuitionistic logic this double-negation elimination does not generally hold. De Morgan's laws describe how negation distributes over conjunction and disjunction: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q and ¬(P ∨ Q) ≡ ¬P ∧ ¬Q. Negation also features in the law of the excluded middle, P ∨ ¬P, in classical logic.

In mathematics and set theory, negation is closely linked to complementation. Given a universal set U, the negation of a predicate P denotes the complement {x ∈ U | ¬P(x)}. It is used to define opposite properties and to form constraints in proofs and algorithms.

In linguistics, negation is realized by negative particles or affixes, words like not or no, and by inflection. The scope of negation determines which part of a sentence is negated, affecting meaning as in It is not raining versus Not all dogs are friendly.

In computing, negation is implemented by the unary not operator (often written as ! or not) for booleans; bitwise negation (~) inverts each bit. Negation underpins conditional expressions, search, and the design of logical circuits and proofs.