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An example of a tautology and how to test it is given in the truth table below for the statement $(P \vee Q) \vee ( \neg P \wedge \neg Q) $
| $P$ |
$Q$ |
$\neg P \wedge \neg Q$ |
$P \vee Q$ |
$(P \vee Q) \vee ( \neg P \wedge \neg Q)$ |
| F |
F |
T |
F |
T |
| F |
T |
F |
T |
T |
| T |
F |
F |
T |
T |
| T |
T |
F |
T |
T |
Thus for whatever truth values P and Q take on, the statement always comes out true as shown in the last coloumn of the truth table.
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