\problemdata                                                             
        {Quantifiers, Logic} % latex-friendly label for the prob.
        {Quantifiers, Logic} % The topic(s) of the problem content.  
        { Rosen, Instructor's resource guide, page 329, exercise 31} % Source (if known)                                          
        {S01 Final, 1} % Usage (list ones you are aware of). 
        {Tina Wang, S02} % Last revision info (author, date).   
                                                                         
                                                                         
\begin{problem}           
Suppose the variable $x$ represents students, $F(x)$ means ``$x$ is a freshman", and $M(x)$ means ``$x$ is a math major". Match \emph{each} statement in the table below with one of the English sentences in this list:

\renewcommand{\labelenumi}{(\arabic{enumi})}
\begin{enumerate}
\item Some freshmen are math majors
\item Every math major is a freshman
\item No math major is a freshman


\end{enumerate}
The first entry in the table has been filled in as an example

\renewcommand{\arraystretch}{2} 
\begin{tabular}{|c|c|c|}
\hline
    & \text{Expression}& Corresponding Sentence \\\hline
 1 & $\forall x [M(x)\implies \neg F(x)]$ &3\\ \hline
 2 & $\neg \exists x [M(x) \And \neg F(x)]$ &\\ \hline
 3 & $\forall x [F(x)\implies \neg M(x)]$& \\ \hline
 4 & $\forall x [M(x)\implies F(x)]$& \\ \hline
 5 & $\exists x [F(x)\And M(x)]$ &\\ \hline
 6 & $\neg \forall x [\neg F(x)\Or \neg M(x)]$& \\ \hline
% 7 & $\forall x [\neg (M(x)\And \neg F(x))]$& \\ \hline
% 8 & $\forall x [\neg M(x) \Or \neg F(x)]$& \\ \hline
% 9 & $\neg \exists x [M(x)\And \neg F(x)]$& \\ \hline
% 10 & $\neg \exists x [M(x)\And F(x)]$ &\\ \hline
% 11 & $\neg \forall x[F(x)\implies \neg M(x)]$& \\ \hline
\end{tabular}

\solution{

\renewcommand{\arraystretch}{2} 
\begin{tabular}{|c|c|c|}
\hline
    & \text{Expression}& Corresponding Sentence \\\hline
 1 & $\forall x [M(x)\implies \neg F(x)]$ &3\\ \hline
 2 & $\neg \exists x [M(x) \And \neg F(x)]$ &2\\ \hline
 3 & $\forall x [F(x)\implies \neg M(x)]$& 3\\ \hline
 4 & $\forall x [M(x)\implies F(x)]$& 2\\ \hline
 5 & $\exists x [F(x)\And M(x)]$ &1\\ \hline
 6 & $\neg \forall x [\neg F(x)\Or \neg M(x)]$&1 \\ \hline
% 7 & $\forall x [\neg (M(x)\And \neg F(x))]$& 2\\ \hline
% 8 & $\forall x [\neg M(x) \Or \neg F(x)]$&3 \\ \hline
% 9 & $\neg \exists x [M(x)\And \neg F(x)]$& 2\\ \hline
% 10 & $\neg \exists x [M(x)\And F(x)]$ &3\\ \hline
% 11 & $\neg \forall x[F(x)\implies \neg M(x)]$& 1\\ \hline
\end{tabular}

}

\end{problem}
                                 