Negation is a truth-functional operator in logic which negates a proposition or formula, rendering its opposite true.
The negation of a proposition, P, may be formalized as:
¬P
This may be read as “not P” or “it is not the case that P”.
In symbolic logic, the negation symbol ( ¬ ) is used to symbolize negation. The tilde ( ˜ ) or the word NOT are used in some systems instead, though ¬ will always be used on this site for consistency.
The following table illustrates the possible truth values of P, and the result of their negation, which always produces the inverse of the original truth value.
| P | ¬P |
|---|---|
| T | F |
| F | T |
In English, the word “not” produces a negation as expected. However, in addition to ¬ there are several other English terms and prefixes that result in negation. The following are some examples of prefixes: