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:

If you have Java, try it out for yourself:

Set the truth values for the propositions P and Q by clicking on the appropriate button beside "P" and "Q" respectively. What is the truth value of Not P? Find out by clicking on the "Compute" button.

P is: T F Q is: T F
Thus, Not P is:

Notice that 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.

17 August 1996