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