Tautology/Examples/Excluded Middle

Example of Tautology

The Law of Excluded Middle:

$p \lor \lnot p$

is an example of a tautology.

Proof

This is conveniently demonstrated by a proof by truth table:

We apply the Method of Truth Tables to the proposition $\vdash p \lor \neg p$.

As can be seen by inspection, the truth value of the main connective, that is $\lor$, is $\T$ for each boolean interpretation for $p$.

$\begin{array}{|c|c|cc|} \hline p & \lor & \neg & p \\ \hline \F & \T & \T & \F \\ \T & \T & \F & \T \\ \hline \end{array}$

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logical truth
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logical truth