

\problemdata     
{S01-PS3-5}           
{relations}              
{}              
{F98-PS3, S01-PS3} 		
{S01 Karger}        	



\begin{problem}  Let $R$ be a binary relation on the set $\{ a, b, c, d, e \}$
defined as follows:

\begin{eqnarray*}
R & =  \{ & (a, a), (a, b), (a, d), (b, a), (b, b), (b, c), (b, d), \\
  & \mbox{} & (c, b), (c, c), (c, d), (d, b), (d, c), (d, d), (e, e) \quad \}
\end{eqnarray*}

Answer yes or no to each of the following questions; if you answer no,
then defend your answer.

\begin{problemparts}
\problempart Is $R$ reflexive?

\solution{
Yes.
}

\problempart Is $R$ symmetric?

\solution{
No. $R$ contains $(a, d)$, but
not $(d, a)$.
}

\problempart Is $R$ transitive?

\solution{
No. $R$ contains $(d, b)$ and $(b, a)$, but not $(d, a)$.  }

\end{problemparts}
\end{problem}
