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\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{$\square$}] There is no correct sequent for which
there is no proof.
\item[\Large{$\square$}] Every sequent has a proof.
\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.
\item[\Large{$\square$}] A sequent has a proof if and only if it
is semantically correct.
\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 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.
\end{itemize}