\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}