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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
\newcommand{\union}{\cup}
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\begin{document}

{\bf Logic 1, WS 2006.
Additional Homework 3, given Nov 9, due Nov 23}

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\noindent
1. 
Prove the correctness of the proof rule ``by contradiction'':

        $$\langle {\cal A},\ \not G \rangle
        \ \ \longrightarrow \ \
        \langle {\cal A} \union \{ G \},\ \or\emptyset \rangle$$


\end{document}
