Principle of Non-Contradiction/Sequent Form/Formulation 2/Proof 2
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Theorem
- $\vdash \neg \paren {p \land \neg p}$
Proof
We apply the Method of Truth Tables to the proposition $\neg \left({p \land \neg p}\right)$.
As can be seen by inspection, the truth value of the main connective, that is $\neg$, is $T$ for each boolean interpretation for $p$.
$\begin{array}{|ccccc|} \hline
\neg & (p & \land & \neg & p)\\
\hline
T & F & F & T & F \\
T & T & F & F & T \\
\hline
\end{array}$
$\blacksquare$