Law of Excluded Middle/Sequent Form/Proof by Truth Table
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Theorem
The Law of Excluded Middle can be symbolised by the sequent:
- $\vdash p \lor \neg p$
Proof
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 $p$.
$\begin{array}{|cccc|} \hline
p & \lor & \neg & p \\
\hline
\F & \T & \T & \F \\
\T & \T & \F & \T \\
\hline
\end{array}$
$\blacksquare$
Sources
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.4$: Statement Forms