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\section*{Written Assignment 2}

\begin{question}{1}
Define the following terms and provide examples of each:
\begin{itemize}
\item Odd integers
\item Even integers
\item Perfect squares
\item Multiples of $d$, for some $d \in \Z$
\item Powers of $t$, for some $t \in \Z$
\item Rational numbers
\item Irrational numbers
\end{itemize}
\end{question}

\begin{question}{2}
Define the following terms:
\begin{itemize}
\item A constructive proof
\item A nonconstructive proof
\item An equivalence proof
\item Proof by contradiction
\end{itemize}
\textbf{Note:} It is not necessary to give examples.
\end{question}

\begin{question}{3}
Is $-135.11\bar{1}$ irrational, as we defined the terms? Why or why not?
\end{question}

\begin{question}{4}
Prove by contradiction that $2\sqrt{2}$ \emph{ is irrational}.\\
\textbf{Hint:} Use the fact that $\sqrt{2}$ is irrational.
\end{question}

\begin{question}{5}
Critique the following false proof:
\begin{align*}
3 &amp; ~&gt;~ 2&amp;\\
3\log_{10}(1/2)&amp; ~&gt;~2\log_{10}(1/2)&amp;\\
\log_{10}(1/2)^3&amp; ~&gt;~\log_{10}(1/2)^2&amp;\\
(1/2)^3&amp; ~&gt;~(1/2)^2&amp;\\
1/8&amp; ~&gt;~1/4&amp;
\end{align*}
\textbf{Hint:} What happens to an inequality when you multiply by a negative number?
\end{question}

\begin{question}{6}
Solve book problem 2.2
\end{question}

\begin{question}{7}
Solve book problem 2.3
\end{question}

\begin{question}{8}
Solve book problem 2.9 (a) and (b)
\end{question}

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