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\begin{titlepage}\begin{centerline}{\Huge \framebox{Burt Rosenberg}}
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\section*{Problem Set \assignmentNumber \hfill{\parbox{3in}
    {\small\sc\begin{flushright} Out: \outdate
     \\ Due: \duedate\end{flushright}}}}


\subsection*{Goals}

Learn predicate logic and its applications to program design.

\subsection*{Reading Assignment}

Read in {\em Program Derivation} sections 2.1, 2.2, in
section 2.3 subsections 2.3.1 through 2.3.3, pages 32--45,
and in section 2.4 subsections 2.4.1 through 2.4.7, pages
54--69.

\subsection*{Written Homework}

\begin{enumerate}
\item Exercise 2.1, pages 82--83.
\item Exercise 2.2, pages 83--84.
\item Prove the following statement:
\begin{theorem} Suppose $\cal F$ and $\cal G$ are two
      tautologically equivalent logical statements, and
      $\cal S$ and $\cal T$ are two Pascal statements or
      statement blocks.
      Then the following two if-then-else statements are equivalent:
\[ \mbox{\tt if $\cal F$ then $\cal S$ else $\cal T$ }\]
\[ \mbox{\tt if $\cal G$ then $\cal S$ else $\cal T$ }\]
\end{theorem}
\item Exercise 2.5, pages 86--87.
\end{enumerate}

\subsection*{An Experiment}

How fast is your unique words program? Its run time depends
on the size of the input. In your \verb.INBOX. are several
files, of several sizes. Try your program on them and
graph the results, size versus run time, connecting the
trial points with lines. 
How can you make the program faster?

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