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37 lines
1.1 KiB
37 lines
1.1 KiB
\item \self Consider the propositional formulas $\varphi = (p \vee q)
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\rightarrow r$, and $\psi = r \vee (\neg p \wedge \neg q)$.
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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|}
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\hline
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$p$&$q$&$r$&$\neg p$&$\neg q$&$p \vee q$&$\neg p \wedge \neg q$&$\varphi$&$\psi$\\
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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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\item Which of the formulas is satisfiable?
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\item Which of the formulas is valid?
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\item Is $\varphi$ equivalent to $\psi$?
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\item Does $\varphi$ semantically entail $\psi$?
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\item Does $\psi$ semantically entail $\varphi$?
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\end{enumerate}
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