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\title{General Mathematics and Computational Science I}
\author{Exercise 1}
\date{September 6, 2005}
\maketitle

\begin{enumerate}
\item (From Ivanov, p.~2) Prove that a checkerboard with $2^n \times
2^n$ squares from which one square has been removed can be covered
exactly by ``triominoes'' of the form
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\end{center}

\item (From Ivanov, p.~2)  Into how many pieces do
\begin{enumerate}
\item $n$ points subdivide a line;
\item $n$ straight lines subdivide the plane, if no two of the lines
are parallel and no three meet in a single point?
\end{enumerate}

\end{enumerate}
\end{document}

\item (From Daepp/Gorkin, p.~114) Let $X$ be a nonempty set with an
equivalence relation $\sim$ on it.  Prove that for all $x,y \in X$, 
\begin{equation*}
  [x] = [y] \qquad \text{if and only if} \qquad x \sim y \,.
\end{equation*}

