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\begin{document}

\centerline{\bf HW 14 CMSC 452}
\centerline{\bf Morally Due TUES May 13 11:00AM} 
\centerline{\bf Dead-Cat Due THU May 15 11:00AM} 


\begin{enumerate}

\item
(30 points) 
(Review the WS1S slides.) 

Give a DFA for the set

$$\{ (x,X) \colon x+1\in X \}.$$

Clearly identify which states are ACCEPT, REJECT, and STUPID.

\newpage

\item
(30 points) 
In this problem all polynomials have integer coefficients and one variable. 

\begin{enumerate}
\item
(10 points)
Is there a polynomial of degree 1 that has a rational root but
does not have an integer root.
If YES then give the polynomial.
If NO then prove NO. 

\item 
(10 points)
Is there a polynomial of degree 1 that has a real root but
does not have a rational root.
If YES then give the polynomial.
If NO then prove NO. 

\item
(10 points)
Is there a polynomial of degree 2 that has a real root but
does not have a rational root.
If YES then give the polynomial.
If NO then prove NO. 

\end{enumerate}

\newpage 

\item
(40 points)

\begin{enumerate}
\item 
(20 points) 
What was your {\bf favorite} part of the course IN THE SECOND HALF (P, NP, Dec, Undec) 
(could be a theorem, a definition, a concept,
whatever mathematical thing you want. It cannot be the GET UP AND DANCE we do during break
or anything else not-math.) 
\item
(20 points) 
What was your {\bf least favorite} part of the course IN THE SECOND HALF (P, NP, Dec, Undec) 
could be a theorem, a definition, a concept,
whatever mathematical thing you want. It cannot be the GET UP AND DANCE we do during break
or anything else not-math.) 
\item
(0 points, not to hand in)
Make up your {\bf cheat sheet} soon so that its not at the last minute.
\end{enumerate}
\end{enumerate}


\end{document}