\documentclass[11pt]{article}

\usepackage{hw}

\begin{document}

\dotitle{8}{Thursday, November 16}


\begin{enumerate}

\item Read section 2.7 of van Dalen.  With example 6 in mind, do problem 10 on page 91.

\item Verify that the following syllogisms are valid by giving deductions.
\begin{enumerate}

\item \begin{quote}
All Greeks are mortal.\\
Some Greeks are women.\\
Therefore, some women are mortal.
\end{quote}

\item \begin{quote}
No Greeks are slaves.\\
Some slaves are women.\\
Therefore, some women are not Greek.
\end{quote}

\end{enumerate}

\item Prove $\neg\forall x\neg\varphi(x)\rightarrow \exists x \varphi(x)$.

\item On page 96, do problem 1(i); on page 99, do problem 6; and on page 102, do problems 3 and 4.

\item Suppose the formula $\psi$ has no free $x$.  Show that $ \forall x \varphi(x)\rightarrow \psi \vdash\forall x(\varphi(x)\rightarrow \psi)$ is \emph{not} provable.

\item\addstar Do problem 7 on page 102.

\end{enumerate}

\end{document}