<exercise>
<statement>
<p>
Let <m>V</m> be the set of all pairs <m>(x,y)</m> of real numbers
together with the following operations:
</p>
<md><mrow><xsl:value-of select="oplus"/></mrow><mrow><xsl:value-of select="otimes"/>.</mrow></md>
<p>
(a) Show that <xsl:value-of select="trueproperty"/>, that is:
</p>
<me>
<xsl:value-of select="truetex"/>.
</me>
<p>
(b) Explain why <m>V</m> nonetheless is not a vector space.
</p>
</statement>
<answer>
<p>
<m>V</m> is not a vector space, which may be shown by demonstrating that
any one of the following properties do not hold:
</p>
<ul>
<xsl:for-each select="falseproperties/*">
<li><xsl:value-of select="."/></li>
</xsl:for-each>
</ul>
</answer>
</exercise>
