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Harvey Mudd College\\
Computer Science \os{80}\\
Logic for Computer Science\\
Fall Semester \os{2002}\\[16pt]

Assignment \#3 -- Propositional Logic: Natural Deduction\\
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Due { \os{11}:\os{00}am}, Monday November \os{4}, \os{2002}
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Give Natural Deduction proofs of each of the following formulas. That is,
give a Natural Deduction proof tree with the given formula as its conclusion,
and no undischarged assumptions. (Note, brackets are used in place of parentheses in
some positions to make the formula nesting structure clearer):

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\begin{enumerate}

\item $([(p \land q) \imp r] \equiv [p\imp(q\imp r)])$

\item $((p \imp q) \imp [(r \imp p)\imp (r\imp q)])$

\item $([(p\imp q)\imp p]\imp p)$

\item $((p\imp r)\equiv [\neg(p\land (\neg r))])$

\item $[(p\imp r)\equiv ((\neg p) \lor r)]$
\end{enumerate}

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