De Morgan's Laws (Logic)/Disjunction/Formulation 1/Proof by Truth Table
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Theorem
- $p \lor q \dashv \vdash \neg \paren {\neg p \land \neg q}$
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.
$\begin{array}{|ccc||cccccc|} \hline p & \lor & q & \neg & (\neg & p & \land & \neg & q) \\ \hline \F & \F & \F & \F & \T & \F & \T & \T & \F \\ \F & \T & \T & \T & \T & \F & \F & \F & \T \\ \T & \T & \F & \T & \F & \T & \F & \T & \F \\ \T & \T & \T & \T & \F & \T & \F & \F & \T \\ \hline \end{array}$
$\blacksquare$