        \problemdata       % Takes 5 *mandatory* arguments
        {validproofs}             % latex-friendly label for the prob.
        {logic, proofs}  % The topic(s) of the problem content.
        {}               % Source (if known)
        {F01 PS1-2, F95 PS1-7, F99} % Usage (list ones you are aware of).
        {}        % Last revision info (author, date).

\begin{problem}
Determine whether each of the following arguments is valid.  If an
argument is correct, what rule of inference (from Rosen, \S~3.1) is
being used?  If it is not, what fallacy (again from Rosen \S~3.1)
occurs?

\begin{problemparts}
\problempart
\emph{Claim}: if $n^2>1$, then $n>1$. \\
{\em Suggested proof:} If $n$ is a real number such that $n>1$, then $n^2>1$.
Suppose that $n^2>1$, then $n>1$.

\solution{Invalid: fallacy of affirming the conclusion.}

\problempart
\emph{Claim}: The number $\log_2 3$ is irrational. \\
{\em Suggested proof:} A number is irrational if it is not the ratio of
two integers. Therefore, since $\log_2 3$ cannot be written in the form
$a/b$ where $a$ and $b$ are integers, it is irrational.

\solution{Invalid: fallacy of affirming the conclusion.}

\problempart
\emph{Claim}: If $n^2 \leq 9$ then, $n \leq 3$. \\
{\em Suggested proof:} Because if $n$ is a real number with $n>3$,
then $n^2 >9$.

\solution{Valid: modus tollens.}

\problempart
\emph{Claim}: If $n\leq 2$, then $n^2\leq 4$.\\
{\em Suggested proof:} Because if $n$ is a real number with $n>2$,
then $n^2>4$.

\solution{Invalid: fallacy of denying the hypothesis.}

\end{problemparts}      

\end{problem}