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\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due December 6, 2013}}
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\emph{Let $S$ be the set of all polynomials on $x$, and let the
  relation $R$ on $S$ be such that $p(x)\mathrel{R}q(x)$ iff $p(x)$
  and $q(x)$ have a real root in common; for instance,
  $(x^2-4x+3)\mathrel R(x^2-6x+9)$, because $x=3$ is a real root of
  both polynomials. Determine (with a proof or with a counterexample,
  as appropriate) whether $S$ is reflexive, symmetric, and/or
  transitive.}


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