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- \noindent DeMorgan's Law can also be proven using the following truth table:
- \begin{displaymath}
- \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
- \hline
- A & B & \neg A & \neg B & (\neg A)\lor(\neg B) & \neg(A \lor B) & \neg(A \land B) & \neg A \land \neg B & \begin{tabular}{@{}c@{}}$\neg(A\land B) \implies$ \\ $ \neg A \lor \neg B$ \end{tabular} & \begin{tabular}{@{}c@{}}$\neg(A\land B) \impliedby$ \\ $ \neg A \lor \neg B$ \end{tabular} \\\hline
- T & T & F & F & F & F & F & F & &\\
- T & F & F & T & T & F & T & F & &\\
- F & T & T & F & T & F & T & F & &\\
- F & F & T & T & T & T & T & T & &\\
- \hline
- \end{array}
- \end{displaymath}
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