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\item \self Consider the propositional formula $\varphi = p \rightarrow
(q \rightarrow r)$.
\begin{enumerate} \item Fill out the truth table for $\varphi$ and its subformulas.
\begin{tabular}{|c|c|c||c|c|c|}\hline$p$&$q$&$r$&$(q \rightarrow r)$&$\varphi=p \rightarrow (q \rightarrow r)$\\\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 ``$\rightarrow$'' connective.\item How can you check whether $\psi$ is semantically equivalent to $\varphi$?
\end{enumerate}
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