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37 lines
988 B
37 lines
988 B
\item \self Consider the propositional formula $\varphi = p \rightarrow
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(q \rightarrow r)$.
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\begin{enumerate}
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\item Fill out the truth table for $\varphi$ and its
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subformulas.
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\begin{tabular}{|c|c|c||c|c|c|}
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\hline
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$p$&$q$&$r$&$(q \rightarrow r)$&$\varphi=p \rightarrow (q \rightarrow r)$\\
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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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\item Is $\varphi$ satisfiable?
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\item Give a formula $\psi$ that is semantically equivalent to
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$\varphi$, but does not use the ``$\rightarrow$'' connective.
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\item How can you check whether $\psi$ is semantically equivalent
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to $\varphi$?
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\end{enumerate}
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