logical negation
Sign in to saveIn 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, \mathord{\sim} P, P^\prime or \overline{P}. It is interpreted intuitively as being true when P is false, and false when P is true. 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.
AI overview
Logical negation is an operation that flips the truth value of a statement—if a statement is true, its negation is false, and vice versa. It matters because negation is a fundamental building block of logical reasoning, allowing us to express opposites and work through complex arguments systematically.
AI-generated from the Wikipedia summary — may contain errors.
Key facts
- Logical connective.title
- Negation
- Logical connective.other titles
- NOT
- Logical connective.wikifunction
- Z10216
- Logical connective.Venn diagram
- Venn10.svg
- Logical connective.definition
- \lnot{x}
- Logical connective.truth table
- (01)
- Logical connective.logic gate
- NOT_ANSI.svg
- Logical connective.DNF
- \lnot{x}
- Logical connective.CNF
- \lnot{x}
- Logical connective.Zhegalkin
- 1 \oplus x
- Logical connective.0 preserving
- no
- Logical connective.1 preserving
- no
Article
17 sectionsContents
- Definition
- Notation
- Precedence
- Properties
- Double negation
- Distributivity
- Linearity
- Self dual
- Negations of quantifiers
- Rules of inference
- Programming language and ordinary language
- Usage in colloquial language
- Kripke semantics
- See also
- References
- Further reading
- External links
{{Infobox logical connective | title = Negation | other titles = NOT | wikifunction = Z10216 | Venn diagram = Venn10.svg | definition = \lnot{x} | truth table = (01) | logic gate = NOT_ANSI.svg | DNF = \lnot{x} | CNF = \lnot{x} | Zhegalkin = 1 \oplus x | 0-preserving = no | 1-preserving = no | monotone = no | affine = yes | self-dual = yes }}
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, \mathord{\sim} P, P^\prime or \overline{P}. It is interpreted intuitively as being true when P is false, and false when P is true. 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.