<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>3.1.8 (Disjunction)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<h3>Disjunction</h3>

<p>We have seen that we can construct larger statements from smaller ones using conjunctions. In fact we can also do this by using a <b>disjunction</b>, this corresponds to the use of the word 'or' in English. </p>
<br/>
<h3>Example</h3>

<p>Consider the statements:</p>
<ol type="A">
<li>It will rain today.</li>
<li>It will rain tomorrow.</li>
</ol>
<p> What is the disjunction of these statements?</p>

<h3>Solution</h3>

<p>The disjunction of the statements reads: C:"It will rain today or it will rain tomorrow."</p>
<br/>
<p>At this point we must make an important distinction. Reading statement \(C\) in English, it seems like it says <i>either</i> it will rain today <i>or</i> it will rain tomorrow, so it will only rain on one day. This is known as an <b>exclusive</b> “or” because it excluded the possibility that it rains on both days, and this is common in the English language.</p>

<p> This is unfortunate, because in mathematics we take \(C\) to mean: either it will rain today or it will rain tomorrow, or both. This is known as an <b>inclusive</b> “or”. In mathematics (unless otherwise stated) it is assumed that a disjunction is <b>inclusive.</b></p>]]></text>
    </questiontext>
    <generalfeedback format="moodle_auto_format">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
