diff --git a/Bookshelf/Enderton/Logic.tex b/Bookshelf/Enderton/Logic.tex index 1cf57f6..3ebb186 100644 --- a/Bookshelf/Enderton/Logic.tex +++ b/Bookshelf/Enderton/Logic.tex @@ -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)]