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\title{General Mathematics and CPS II}
\author{Exercise 10}
\date{March 6, 2015}
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\begin{enumerate}

\item Let $G$ be a group, and let $H$ and $K$ be subgroups of $G$.
Show that $H \cap K$ is also a subgroup of $G$.

\item (Ivanov, p. 41, Exercise.)  Let $R_\alpha$ denote the reflection
about the line $x=\alpha$.  Let $G$ be the (symmetry) group generated
by the unit translation along the $x$-axis and by $R_0$.  Show that
$R_\alpha \in G$ if and only if $2 \alpha \in \mathbb{Z}$.


\item Draw an ornament corresponding to each of the seven ornament
groups, see Ivanov pp.~41--42.  Make sure that each example has
precisely the symmetries of the respective case, and no more.


\end{enumerate}
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