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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}%
\hyperlabel{sec:exercises-1}
\subsection{\sorry{Exercise 1.1}}%
\hyperlabel{sub:exercise-1.1}
\subsection{\sorry{Exercise 1.1.1}}%
\hyperlabel{sub:exercise-1.1.1}
Give three sentences in English together with translations into our formal
language.
@ -118,8 +118,8 @@ The sentences shoudl be chosen so as to have an interesting structure, and the
\end{answer}
\subsection{\sorry{Exercise 1.2}}%
\hyperlabel{sub:exercise-1.2}
\subsection{\sorry{Exercise 1.1.2}}%
\hyperlabel{sub:exercise-1.1.2}
Show that there are no wffs of length 2, 3, or 6, but that any other positive
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}
\subsection{\sorry{Exercise 1.3}}%
\hyperlabel{sub:exercise-1.3}
\subsection{\sorry{Exercise 1.1.3}}%
\hyperlabel{sub:exercise-1.1.3}
Let $\alpha$ be a wff; let $c$ be the number of places at which binary
connective symbols $(\land, \lor, \Rightarrow, \Leftrightarrow)$ occur in
@ -146,8 +146,8 @@ Show by using the induction principle that $s = c + 1$.
\end{answer}
\subsection{\sorry{Exercise 1.4}}%
\hyperlabel{sub:exercise-1.4}
\subsection{\sorry{Exercise 1.1.4}}%
\hyperlabel{sub:exercise-1.1.4}
Assume we have a construction sequence ending in $\phi$, where $\phi$ does not
contain the symbol $A_4$.
@ -161,8 +161,8 @@ Show that the result is still a legal construction sequence.
\end{answer}
\subsection{\sorry{Exercise 1.5}}%
\hyperlabel{sub:exercise-1.5}
\subsection{\sorry{Exercise 1.1.5}}%
\hyperlabel{sub:exercise-1.1.5}
Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$.
\begin{enumerate}[(a)]
@ -179,8 +179,8 @@ Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$.
\end{answer}
\subsection{\sorry{Exercise 1.6}}%
\hyperlabel{sub:exercise-1.6}
\subsection{\sorry{Exercise 1.1.6}}%
\hyperlabel{sub:exercise-1.1.6}
Suppose that $\alpha$ is a wff not containing the negation symbol $\neg$.
\begin{enumerate}[(a)]