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\item \lect Consider the propositional formula $\varphi = (p \wedge q)
\rightarrow (q \vee \neg r)$. Fill out the truth table for $\varphi$ and its
subformulas.
\begin{tabular}{|c|c|c||c|c|c||c|}\hline$p$&$q$&$r$&$p\wedge q$&$\neg r$&$q \vee \neg r$&$\varphi = (p \wedge q)\rightarrow (q \vee \neg r)$\\\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}
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