V1.xml

<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
  <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>
      <me>{{#oplus}}{{.}}{{/oplus}}</me><me>{{#otimes}}{{.}}{{/otimes}}.</me>
    <p>
      (a) Show that {{trueproperty}}, that is:
    </p>
    <me>
      {{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>
          {{#falseproperties}}
        <li>{{.}}</li>
          {{/falseproperties}}
    </ul>
  </answer>
</exercise>