De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 2/Proof by Truth Table

Theorem

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

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connective is true for all boolean interpretations.

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