\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}