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\centerline{MATH 243 -- Mathematical Structures}
\centerline{Practice on Statements with Quantifiers}
\centerline{September 6, 2017}
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\noindent
For each of the following statements with quantifiers:
\begin{enumerate}
\item[(1)] Give the negation, and 
\item[(2)] For the ones where it is possible, 
decide whether or not the original statement is true. 
Explain your reasoning.
\end{enumerate}
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\noindent
{\it Statements}
\vskip 10pt
\begin{enumerate}
\item[A)]  Every student in this class is female.
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\item[B)]  All the children received Valentine's Day cards or candy.
\vskip 20pt
\item[C)]  For every real number $x$, the square of $x$ is strictly positive.
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\item[D)]  There exists a pair of real numbers $x$ and $y$ such that $x > y$ and
$x^2 < y^2$.  
\vskip 20pt
\item[E)]  There exists a real number $x > 0$ such that for all real numbers 
$y > 0$, $x \le y$. 
\end{enumerate}
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