If p is a statement, then the statement ‘not p’, denoted by ¬p, is the negation of p. It states, in some suitable wording, the opposite of p. For example, if p is ‘It is raining’, then ¬p is ‘It is not raining’; if p is ‘r > 2’, then ¬p is ‘r ≤2’. If p is true then ¬p is false, and vice versa. So the truth table of ¬p is:
See De Morgan’s laws.
1. In arithmetic, the operation of changing the sign of a nonzero arithmetic quantity; the negation of zero is zero. Negation is usually denoted by the minus sign.
2. In logic, the application of the NOT operation on a statement, truth value, or formula.
The negation of a proposition is its denial: classically, that proposition which is true when it is false, and false when it is true. The sign ¬ (for alternatives see Appendix 1: Logical Symbols) expresses a truth function, defined in the table:
A proposition may be controverted in other ways than by asserting its strict negation. For instance ‘that’s red’, is controverted by ‘that’s green’, since both cannot be true together. But both can be false and one is not the direct denial of the other. See contrary, square of opposition.
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