De Morgan's Laws (Logic)/Conjunction of Negations/Formulation 1/Proof by Truth Table

Theorem

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

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.

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