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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 $\phi$ fromthe 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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