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%% Practice Problems 4: Partial Orders, Graphs, DAGs 
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\textbf{Reading:} Rosen~\S6.6, Week~4 Lecture notes.
\emph{Supplementary reading:} Velleman~\S4.4, Rosen~\S7.1--7.4, 7.8.

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By~9am on the due date, send email to
\begin{center}
\texttt{6042-probs@theory.lcs.mit.edu}
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indicating in at most three sentences one or more of the following:
the passage in the reading---\emph{including its page number}---you
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\item found most difficult,
\item found most surprising,
\item would like to have discussed in the next Lecture.
\end{itemize}
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%\textbf{Problem Submission:} We are trying out a \textbf{new online tutor
%system} for submission of the pre-lecture practice problems.  You can
%access the tutor from the course website.  The online tutor will tell you
%if your answers to the problems are correct, and it will allow you to
%change the incorrect ones.
%
%This version of the tutor is a beta-release.  If you have trouble using
%the online system, feel free to submit your problem solutions on paper at
%the beginning of your tutorial section.  We would be grateful for a bug
%report on any problems with the online tutor.
\fi

\begin{problems}

\problem Rosen Exercise 6.6.26 (a,b,e).
\solnospace{(a) 27,48,60,72. (b) 2,9. (e) 18,36,72.}

\problem Rosen Exercise 7.2.20.
\solnospace{7.}

\problem Rosen Exercises 7.3.35 and 7.3.36.
\solnospace{The graphs are isomorphic in~7.3.35 but non-isomorphic in~7.3.36.}

\problem Rosen Exercise 7.4.15. 
\solnospace{c.}

\problem Rosen Exercise 7.8.4.
\solnospace{3.}

\end{problems}

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