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\newcommand{\Q}{\mathbb{Q}}
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\begin{document}

\begin{center}
\includegraphics[width=0.5in]{../ltr-logo.jpg}
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\noindent{\Large{\textsc{Intro to Abstract Mathematics\hfill Assignment 2.3  \\ Spring 2020 \hfill Due February 5}}}

\large

\vspace{1cm}


\begin{exercise}
Find the truth sets of the following statements (i) if the universe of discourse is $\Z$ and (ii) if the universe of discourse is $\R$.

\begin{itemize}

\item[\bf a.]  $x^2<3$.

\item[\bf b.]  $x^2>x$.

\item[\bf c.]  $2x+1=0$.

\end{itemize}

\end{exercise}

\begin{exercise}
Find the truth set of the two-variable statement $P(x,c): x^2 + x + c \le 0$, if the universe of discourse is $\R$.
\end{exercise}

\begin{exercise}
Show that $\{c \in \R \,| \, x^3 -3x + c = 0 \text{ has exactly two real solutions} \} = \{ \pm 2 \}$.  [{\em Suggestion:}  Think about the shape of the graph of the function $f(x) = x^3 - 3x + c$.]
\end{exercise}

\begin{exercise}
Textbook exercise 1.3.9.
\end{exercise}

\end{document}
