Summary

Any proposition P can be converted into its negation with a negation operator, producing the new, complex, proposition:

Not P

The proposition Not P is true if and only if P is false. It is false only if P is true. The truth table for Not P is as follows:

Examples

P	Q	Not P
T	T	F
T	F	F
F	T	T
F	F	T

Proof

It does not matter whether Q is true or false. Every time, Not P is true if P is false, and false if P is true.