Principle of Non-Contradiction/Sequent Form/Formulation 2/Proof 2

Theorem

 * $\vdash \neg \left({p \land \neg p}\right)$

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 $p$.

$\begin{array}{|ccccc|} \hline \neg & (p & \land & \neg & p)\\ \hline T & F & F & T & F \\ T & T & F & F & T \\ \hline \end{array}$