If P is a proposition, then ~P is true if P is false and it is false if P is true. ~P is called the negation of P.
The law that states that every proposition is either true or false. ( Study 5)
A truth-functional operation, symbolized by the truth-functional symbol "~" and usually translated "not." The negation of a claim is true if and only if the claim is false.
In logic and mathematics, negation is an operation on logical values, for example, the logical value of a proposition, that sends true to false and false to true. Intuitively, the negation of a proposition holds exactly when that proposition does not hold.
In rhetoric, where the role of the interpreter is taken into consideration as a non-negligible factor, negation bears a much wider range of functions and meanings than it does in logic, where the interpretation of signs for negation is constrained by axioms to a few standard options, typically just the classical definition and a few schemes of intuitionism.