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\item Explain what it means that natural deduction for propositional logic is \emph{sound}? \newline
\item The soundness of natural deduction for propositional logic can be proven via a mathematical induction proof.
Discuss the proof idea by stating the \emph{induction hypothesis}, and what needs to be shown for the \emph{induction base-case} as well as for the \emph{induction step}.

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