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36 lines
1.1 KiB
36 lines
1.1 KiB
\item \lect Consider the propositional formulas $\varphi = (p \rightarrow
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q) \vee \neg r$ and $\psi = (\neg r \wedge p) \vee (\neg q \rightarrow \neg r)$.
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\begin{enumerate}
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\item Fill out the truth table for $\varphi$ and $\psi$ and
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their subformulas.
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\begin{tabular}{|c|c|c||c|c|c|c|c||c|c|}
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\hline
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$p$&$q$&$r$&$\neg q$&$\neg r$&$p \rightarrow q$&$\neg r \wedge p$&$\neg q \rightarrow \neg r$&$\varphi$&$\psi$\\
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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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\vspace{0.5cm}
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\item Which of the formulas is satisfiable?
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\item Which of the formulas is valid?
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\item Which of the two formulas $\varphi$ and $\psi$ entails the other?
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\end{enumerate}
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