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\item \self Consider the propositional formula $\phi = (p \lor \lnot q) \imp (\lnot p \land \lnot r)$. Fill out the truth table for $\phi$ and its subformulas. Compute a CNF as well as a DNF for $\phi$ from the truth table.
\begin{tabular}{|c|c|c||c|c|c|c|c||c|} \hline $p$ & $q$ & $r$ & $\lnot q$ & $p \lor \lnot q$ & $\lnot p$ & $\lnot r$ & $\lnot p \land \lnot r$ & $\phi = (p \lor \lnot q) \imp (\lnot p \land \lnot r)$\\ \hline \hline \textbf{F} &\textbf{F} &\textbf{F} & & & & & &\\ \hline \textbf{F} &\textbf{F} &\textbf{T} & & & & & &\\ \hline \textbf{F} &\textbf{T} &\textbf{F} & & & & & &\\ \hline \textbf{F} &\textbf{T} &\textbf{T} & & & & & &\\ \hline \textbf{T} &\textbf{F} &\textbf{F} & & & & & &\\ \hline \textbf{T} &\textbf{F} &\textbf{T} & & & & & &\\ \hline \textbf{T} &\textbf{T} &\textbf{F} & & & & & &\\ \hline \textbf{T} &\textbf{T} &\textbf{T} & & & & & &\\ \hline \end{tabular}
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