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Feb 19th, 2019
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  1. \noindent DeMorgan's Law can also be proven using the following truth table:
  2.  
  3. \begin{displaymath}
  4. \begin{array}{|c|c|c|c|c|c|c|c|c|c|}
  5. \hline
  6. 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
  7. T & T & F & F & F & F & F & F & &\\
  8. T & F & F & T & T & F & T & F & &\\
  9. F & T & T & F & T & F & T & F & &\\
  10. F & F & T & T & T & T & T & T & &\\
  11. \hline
  12. \end{array}
  13. \end{displaymath}
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