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Negation (NOT) ○◂｜Definition｜1st｜20251119205401-00-⌔

Negation - Wikipedia

Negation

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In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition $P$ to another proposition “not $P$”, written $\neg P$, $\sim P$, $P^{\prime }$¹ or $\overline{P}$². It is interpreted intuitively as being true when $P$ is false, and false when $P$ is true.³⁴ For example, if $P$ is “The dog runs”, then “not $P$” is “The dog does not run”. An operand of a negation is called a negand or negatum.⁵

Negation is a unary logical connective. It may furthermore be applied not only to propositions, but also to notions, 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 $P$ is the proposition whose proofs are the refutations of $P$.

Printed 2026-06-28.

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Footnotes

1. Virtually all Turkish high school math textbooks use p’for negation due to the books handed out by the Ministry of National Education representing it as p’. ↩

2. “NEGATION definition and meaning | Collins English Dictionary”. www.collinsdictionary.com. 15 December 2025. Retrieved 20 December 2025. ↩

3. Weisstein, Eric W. “Negation”. mathworld.wolfram.com. Retrieved 2 September 2020. ↩

4. “Logic and Mathematical Statements - Worked Examples”. www.math.toronto.edu. Retrieved 2 September 2020. ↩

5. Beall, Jeffrey C. (2010). Logic: the basics (1. publ ed.). London: Routledge. p. 57. ISBN 978-0-203-85155-5. ↩

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