Questionnaire-2024/natural_deduction_propositional_logic/1002_sol.tex

\begin{enumerate}
\item
	\begin{quote}
	    This sequent is provable.

        \begin{logicproof}{1}
            (p \land q) \land \lnot r & \prem \\
            p \land q & $\ande{1} 1 $\\
            q & $\ande{2} 2$ \\
            q \lor r & $\ori{1} 3$
        \end{logicproof}
	\end{quote}
\item
	\begin{quote}
        This sequent is not provable.

        $\mathcal{M} : p = T, q = T, r = F$ \\
        $\mathcal{M} \models (p \lor q) \land \lnot r$ \\
        $\mathcal{M} \nmodels q \land r$
    \end{quote}
\end{enumerate}