You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
37 lines
946 B
37 lines
946 B
\item \self Consider the propositional formula $\varphi = p \imp
|
|
(q \imp r)$.
|
|
|
|
\begin{enumerate}
|
|
\item Fill out the truth table for $\varphi$ and its
|
|
subformulas.
|
|
|
|
\begin{tabular}{|c|c|c||c|c|c|}
|
|
\hline
|
|
$p$&$q$&$r$&$(q \imp r)$&$\varphi=p \imp (q \imp r)$\\
|
|
\hline
|
|
\hline
|
|
\textbf{F} &\textbf{F} &\textbf{F} & & \\
|
|
\hline
|
|
\textbf{F} &\textbf{F} &\textbf{T} & & \\
|
|
\hline
|
|
\textbf{F} &\textbf{T} &\textbf{F} & & \\
|
|
\hline
|
|
\textbf{F} &\textbf{T} &\textbf{T} & & \\
|
|
\hline
|
|
\textbf{T} &\textbf{F} &\textbf{F} & & \\
|
|
\hline
|
|
\textbf{T} &\textbf{F} &\textbf{T} & & \\
|
|
\hline
|
|
\textbf{T} &\textbf{T} &\textbf{F} & & \\
|
|
\hline
|
|
\textbf{T} &\textbf{T} &\textbf{T} & & \\
|
|
\hline
|
|
\end{tabular}
|
|
|
|
\item Is $\varphi$ satisfiable?
|
|
\item Give a formula $\psi$ that is semantically equivalent to
|
|
$\varphi$, but does not use the ``$\imp$'' connective.
|
|
\item How can you check whether $\psi$ is semantically equivalent
|
|
to $\varphi$?
|
|
|
|
\end{enumerate}
|