Questionnaire-2024/natural_deduction_propositional_logic/0058.tex

\item \self Natural deduction for propositional logic is sound and
    complete. In the following list, mark each statement with either
    \textbf{S}, \textbf{C}, \textbf{B}, or \textbf{N}, depending on
    whether the corresponding statement follows from
    \textbf{S}oundness, \textbf{C}ompleteness, \textbf{B}oth, or
    \textbf{N}either.
    (Note: If a statement is in itself factually wrong, or has nothing to do with soundness and completeness, mark it
    \textbf{N}, since it follows from neither soundness nor completeness.)

\begin{itemize}
\item[\Large{$\square$}] A sequent has a proof if and only if it
    is semantically correct.
\item[\Large{$\square$}] If a model satisfies the premise(s) of a
    given sequent, but does not satisfy the conclusion of the
    sequent, it is not possible to construct a proof for the
    sequent.
\item[\Large{$\square$}] There is no correct sequent for which
    there is no proof.
\item[\Large{$\square$}] Every sequent has a proof.
\item[\Large{$\square$}] An incorrect sequent does not have a
    proof.
\item[\Large{$\square$}] Every propositional formula is either
    valid or not valid.
\item[\Large{$\square$}] If all models that satisfy the premise(s)
    of a given sequent also satisfy the conclusion of the
    sequent, there exists a proof for the sequent.
\end{itemize}