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She was arrested, tried, convicted, and fined $100, which she refused to pay. Nevertheless, it served its purpose. “I only know that it was the password I used, and all of them that I took over told it to me before I took them.” The dangers increased as Gragston continued his work. If you have trouble trying to prove one of the two directions directly, try proving its contrapositive instead. \end{clue} % % Hints for Chapter 3 of "A Problem Course in Mathematical Logic" % \subsection*{Hints for Chapter~\ref{ch:three}} \begin{clue}{p:axta} Truth tables are probably the best way to do this. \end{clue} \begin{clue}{p:snd} Look up Proposition \ref{p:tif}. \end{clue} \begin{clue}{p:ded} There are usually many different deductions with a given conclusion, so you shouldn't take the following hints as gospel. \begin{enumerate} \item Use A2 and A1. \item Recall what $\lor$ abbreviates. \end{enumerate} \end{clue} \begin{clue}{p:three3a} You need to check that $\varphi_1 \dots \varphi_\ell$ satisfies the three conditions of Definition~\ref{d:ded}; you know $\varphi_1 \dots \varphi_n$ does. \end{clue} \begin{clue}{p:dmp} Put together a deduction of $\beta$ from $\Gamma$ from the deductions of $\delta$ and $\delta \to \beta$ from $\Gamma$. \end{clue} \begin{clue}{p:three5} Examine Definition \ref{d:ded} carefully. \end{clue} \begin{clue}{p:three6} The key idea is similar to that for proving Proposition \ref{p:dmp}. \end{clue} \begin{clue}{t:ded} One direction follows from Proposition \ref{p:dmp}.
Pages: 256
Publisher: St. Martin's Press; First Edition edition (September 16, 2008)
ISBN: 0230602886
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