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9 months ago
  1. \begin{tabular}{|c|c|c||c|c|c||c|}
  2. \hline
  3. $p$&$q$&$r$&$\lnot p$&$r \lor \lnot p$&$q \imp p$&$\phi$\\
  4. \hline
  5. \hline
  6. \textbf{F} &\textbf{F} &\textbf{F} & \textbf{T} & \textbf{T} & \textbf{T} & \textbf{T} \\
  7. \hline
  8. \textbf{F} &\textbf{F} &\textbf{T} & \textbf{T} & \textbf{T} & \textbf{T} & \textbf{T} \\
  9. \hline
  10. \textbf{F} &\textbf{T} &\textbf{F} & \textbf{T} & \textbf{T} & \textbf{F} & \textbf{F} \\
  11. \hline
  12. \textbf{F} &\textbf{T} &\textbf{T} & \textbf{T} & \textbf{T} & \textbf{F} & \textbf{F} \\
  13. \hline
  14. \textbf{T} &\textbf{F} &\textbf{F} & \textbf{F} & \textbf{F} & \textbf{T} & \textbf{F} \\
  15. \hline
  16. \textbf{T} &\textbf{F} &\textbf{T} & \textbf{F} & \textbf{T} & \textbf{T} & \textbf{T} \\
  17. \hline
  18. \textbf{T} &\textbf{T} &\textbf{F} & \textbf{F} & \textbf{F} & \textbf{T} & \textbf{F} \\
  19. \hline
  20. \textbf{T} &\textbf{T} &\textbf{T} & \textbf{F} & \textbf{T} & \textbf{T} & \textbf{T} \\
  21. \hline
  22. \end{tabular}
  23. \begin{equation*}
  24. \begin{split}
  25. \textit{CNF}(\phi) = & (p \lor \lnot q \lor r) \\
  26. \land & (p \lor \lnot q \lor \lnot r) \\
  27. \land & (\lnot p \lor q \lor r) \\
  28. \land & (\lnot p \lor \lnot q \lor r) \\
  29. \end{split}
  30. \end{equation*}