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27 lines
859 B
27 lines
859 B
\item \self Consider the propositional formula $\phi = (\lnot(\lnot a
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\land b) \land \lnot c)$. 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|}
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\hline
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$a$&$b$&$c$&$\lnot a$&$\lnot a \land b$&$\lnot(\lnot a \land b)$&$\lnot c$&$\phi = (\lnot(\lnot a \land b) \land \lnot c)$\\
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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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