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Enderton (logic). Fix up exercise numbering.

finite-set-exercises
Joshua Potter 2023-08-08 14:52:52 -06:00
parent 8f15ec7d6d
commit b91ee81261
1 changed files with 12 additions and 12 deletions
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Bookshelf/Enderton/Logic.tex
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@ -104,8 +104,8 @@ If $S$ is a set of wffs containing all the sentence symbols and closed under all
\section{Exercises 1}% \section{Exercises 1}%
\hyperlabel{sec:exercises-1} \hyperlabel{sec:exercises-1}
\subsection{\sorry{Exercise 1.1}}% \subsection{\sorry{Exercise 1.1.1}}%
\hyperlabel{sub:exercise-1.1} \hyperlabel{sub:exercise-1.1.1}
Give three sentences in English together with translations into our formal Give three sentences in English together with translations into our formal
language. language.
@ -118,8 +118,8 @@ The sentences shoudl be chosen so as to have an interesting structure, and the
\end{answer} \end{answer}
\subsection{\sorry{Exercise 1.2}}% \subsection{\sorry{Exercise 1.1.2}}%
\hyperlabel{sub:exercise-1.2} \hyperlabel{sub:exercise-1.1.2}
Show that there are no wffs of length 2, 3, or 6, but that any other positive Show that there are no wffs of length 2, 3, or 6, but that any other positive
length is possible. length is possible.
@ -130,8 +130,8 @@ Show that there are no wffs of length 2, 3, or 6, but that any other positive
\end{answer} \end{answer}
\subsection{\sorry{Exercise 1.3}}% \subsection{\sorry{Exercise 1.1.3}}%
\hyperlabel{sub:exercise-1.3} \hyperlabel{sub:exercise-1.1.3}
Let $\alpha$ be a wff; let $c$ be the number of places at which binary Let $\alpha$ be a wff; let $c$ be the number of places at which binary
connective symbols $(\land, \lor, \Rightarrow, \Leftrightarrow)$ occur in connective symbols $(\land, \lor, \Rightarrow, \Leftrightarrow)$ occur in
@ -146,8 +146,8 @@ Show by using the induction principle that $s = c + 1$.
\end{answer} \end{answer}
\subsection{\sorry{Exercise 1.4}}% \subsection{\sorry{Exercise 1.1.4}}%
\hyperlabel{sub:exercise-1.4} \hyperlabel{sub:exercise-1.1.4}
Assume we have a construction sequence ending in $\phi$, where $\phi$ does not Assume we have a construction sequence ending in $\phi$, where $\phi$ does not
contain the symbol $A_4$. contain the symbol $A_4$.
@ -161,8 +161,8 @@ Show that the result is still a legal construction sequence.
\end{answer} \end{answer}
\subsection{\sorry{Exercise 1.5}}% \subsection{\sorry{Exercise 1.1.5}}%
\hyperlabel{sub:exercise-1.5} \hyperlabel{sub:exercise-1.1.5}
Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$. Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$.
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
@ -179,8 +179,8 @@ Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$.
\end{answer} \end{answer}
\subsection{\sorry{Exercise 1.6}}% \subsection{\sorry{Exercise 1.1.6}}%
\hyperlabel{sub:exercise-1.6} \hyperlabel{sub:exercise-1.1.6}
Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$. Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$.
\begin{enumerate}[(a)] \begin{enumerate}[(a)]