Questionnaire-2024/natural_deduction_propositional_logic/0015_sol.tex

Translation: \\
$p:$ \quad Press button. \\
$q:$ \quad Open window. 
\begin{tabbing}
    If I press the button, the window opens. \quad \= $p \imp q$ \\
    The window is open. \> $q$ \\
    Therefore, I pressed the button. \> $\vdash p$ 
\end{tabbing}

\emph{sequent:} \quad $p \imp q, q \vdash p$ \\

This sequent is not provable.

$\mathcal{M} : p = F, q = T$ \\
$\mathcal{M} \models p \imp q, q$ \\
$\mathcal{M} \nmodels p$