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COMPUTER SCIENCE 20, SPRING 2012 \\
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\\
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Class \#17 (Graphs and Relations)
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\paragraph{Homework, due in hard copy Friday 3/9/2012 at 10:10am}
\paragraph{Please write your TF's name on your homework, and list the names of any students with whom you collaborated.}
\begin{enumerate}
\item A directed tree, as defined previously, is a special type of directed graph that has the following properties:
\begin{itemize}
\item there is exactly one node of in-degree 0, which we will call the root
\item for any vertex $V$ in the tree, there is exactly one walk from the root to $V$
\end{itemize}
For each of the following properties, describe the subset of directed trees that represent a relationship with the given property, and prove that no other tree can have the property. (Hint: most trees will not satisfy most of these properties.)
\begin{enumerate}
\item Transitive
\item Reflexive
\item Symmetric
\item Antisymmetric
\end{enumerate}
\end{enumerate}
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