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.
|
|
\item \self Consider the propositional formula $\varphi = (p \imp q)
\land(q \imp r) \land (\neg r \lor p)$.
\begin{enumerate} \item Fill out the truth table for $\varphi$ (and its subformulas).
\begin{tabular}{|c|c|c||c|c|c|c|c|}\hline$p$&$q$&$r$&$(p \imp q)$&$(q \imp r)$&$\;\neg r\;$&$(\neg r \lor p)$&$\quad\varphi\quad$\\\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 Is $\varphi$ valid?\item Give a formula $\psi$ that semantically entails $\varphi$ (i.e., it should be the case that $\psi \models \varphi$).\item How can you check, using a truth table, whether $\psi$ semantically entails $\varphi$?
\end{enumerate}
|
