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Logical Operators

Negation (not)

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.