negation

/ni'geiʃn/
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negation

The student wrote the negation of the statement on the board.

Definition
  1. Noun:
    • (Logic) A proposition that is true if and only if another proposition is false: In formal logic, a "negation" is a statement that directly contradicts another statement, creating an opposite truth value.
    • The speech act of negating: The action of denying, refusing, or contradicting something through language.
    • A negative statement; a statement that is a refusal or denial of some other statement: An utterance or declaration that expresses contradiction, denial, or opposition to a previous claim or idea.
Usage Examples
  • Noun (Logical Proposition):

    • The negation of the statement "It is raining" is "It is not raining."
    • In the truth table, the negation column shows the opposite values.
  • Noun (Speech Act):

    • Her sharp negation of the accusation ended the debate.
    • The act of negation is fundamental to critical argument.
  • Noun (Negative Statement):

    • His answer was a simple negation: "No, I did not."
    • The document contained a formal negation of the earlier claims.
Advanced Usage
  • "Double Negation": In logic and some languages, using two negatives which can result in an affirmative or emphasize the negative.

    • In standard English, "I don't know nothing" is often considered a non-standard double negation meaning "I don't know anything."
  • "Negation as Failure": A concept in logic programming where something is assumed false if it cannot be proven true.

    • The system uses negation as failure to conclude an event did not occur.
Variants and Related Words
  • Negate (verb): To nullify, deny, or make ineffective.

    • The new evidence may negate the previous theory.
  • Negative (adjective): Expressing denial, refusal, or absence; characterized by a lack of positive qualities.

    • She received a negative response to her request.
  • Negativity (noun): The expression of criticism or pessimism; the character of being negative.

    • Try to avoid negativity in the workplace.
Synonyms
  • Denial: A statement that something is not true or does not exist.
  • Contradiction: A combination of statements, ideas, or features that are opposed to one another.
  • Refusal: An act of expressing unwillingness to do something.
  • Rejection: The dismissing or refusing of a proposal, idea, etc.
Antonyms
  • Affirmation: A declaration that something is true; a positive assertion.
  • Confirmation: The action of confirming something; establishing the truth or validity.
  • Assertion: A confident and forceful statement of fact or belief.
Related Phrases and Concepts
  • Logical Negation (Symbol: ¬, ~): The operation in logic that takes a proposition to another proposition "not P".

    • The symbol ¬P represents the logical negation of proposition P.
  • Negation of a Quantifier: In predicate logic, the rules for negating statements with "for all" (∀) and "there exists" (∃).

    • The negation of "All cats are black" is "There exists a cat that is not black."
negation

The student wrote the negation of the statement on the board.

Noun
  1. (logic) a proposition that is true if and only if another proposition is false
  2. the speech act of negating
  3. a negative statement; a statement that is a refusal or denial of some other statement