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\pset{1}{February 2, 1999; revised 2/5/99}{2:35pm in lecture, February 9, 1998}

\textbf{Reading}: \emph{The Nuts and Bolts of Proofs}, pp. 1--40; the
Rosen text, \S 1.1--1.5, 2.3, and 3.1 (this applies to both the third and
fourth editions).

The reading assignment for this problem set is 88 pages from Rosen and 40
pages from \emph{Nuts and Bolts} --- an awful lot even by 6.042J/18.062J
standards \texttt{:-)}.  Most of this reading reviews elementary
mathematical topics which should be familiar to you; you can skim these.
Do look more closely at any topics which seem unfamiliar, and if there are
many such topics, we encourage you to discuss this with your TA so he can
help you plan a catch up strategy.

\medskip

Do the following problems from the Rosen textbook, \emph{\textbf{third
edition}}.  (If you do not have the third edition, see the course web page
for the full problem texts.)

\begin{problems}

\problem \S 1.1, Exercise 28.  Carefully explain your answer.

\problem \S 1.2, Exercise 36.

\problem \S 1.3, Exercise 10.

\problem \S 1.3, Exercise 26.

\problem \S 1.4, Exercise 12.

\problem Prove that $\card{A \oplus B} = \card{A} + \card{B} - 2\card{A
\cap B}$.  \hint See \S1.5, paragraph following Example 5.

\problem \S 1.5, Exercise 26.

\problem \S 2.3, Exercise 34.

\problem \S 3.1, Exercise 18.

\end{problems}

Remember to include a \emph{collaboration statement} on the front page of
your solutions (see Handout 2, \emph{Course Information}).

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