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\renewcommand{\not}{\neg}
\renewcommand{\and}{\wedge}
\renewcommand{\or}{\vee}
\newcommand{\impl}{\Rightarrow}
\newcommand{\lequiv}{\Leftrightarrow} %equivalence as logical connective
\newcommand{\all}{\forall}
\newcommand{\exi}{\exists}
\newcommand{\elc}{\models}  % semantic logical consequence
\newcommand{\ylc}{\vdash}  % syntactic logical consequence
%\equiv is already defined for === semantic equivalence
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\begin{document}

{\bf Logic 1, WS 2008.
Homework 5, given Nov 27, due Dec 4.}

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1.
Prove the reversibility of the rules $\and\ylc,\ \not\ylc,\ \ylc\not.$

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2.
Find rules for $\or\ylc,\ \ylc\or$ and prove their reversibility.

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3.
Show how to eliminate $\or\ylc$ by reducing it to rules from the ``small'' calculus.

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4.
Find by elimination the rules for {\em modus tollens} and for {\em unit resolution} and investigate which formula can be deleted.

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