U+00AC Not Sign

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In logic, negation, also called the logical complement, is an operation that takes a proposition P {displaystyle P} to another proposition "not P {displaystyle P} ", written ¬ P {displaystyle eg P} , ∼ P {displaystyle {mathord {sim }}P} or P ¯ {displaystyle {overline {P}}} . It is interpreted intuitively as being true when P {displaystyle P} is false, and false when P {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 P {displaystyle P} is the proposition whose proofs are the refutations of P {displaystyle P} .