Questionnaire-2024/natural_deduction_propositional_logic/0003_sol.tex

This sequent is provable.

\emph{Solution 1:}
\begin{logicproof}{2}
    p \land q & prem. \\
    \lnot q \land r & prem. \\
    p & $\land$e1 1 \\
    r & $\land$e2 2 \\
    \lnot \lnot p & $\lnot \lnot$i 3 \\
    \lnot \lnot r & $\lnot \lnot$i 4 \\
    \lnot \lnot p \land \lnot \lnot r & $\land$i 5,6
\end{logicproof}

\emph{Solution 2:}
\begin{logicproof}{2}
    p \land q & prem. \\
    \lnot q \land r & prem. \\
    q & $\land$e2 1 \\
    \lnot q & $\land$e1 2 \\
    \bot & $\lnot$e 3,4 \\
    \lnot \lnot p \land \lnot \lnot r & $\bot$e 5
\end{logicproof}