<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-mutually-exclusive-sets" target="_blank">Mutually Exclusive Sets Exercise</a></p>
<p><strong>Note</strong>: around 2 minutes and 30 seconds into the video, Greg says that the sets of integers and solutions to the equation a<sup>3</sup> + b<sup>3</sup> = c<sup>3</sup> are mutually exclusive. This is true only if a, b and c are positive - which we forgot to mention.</p><p><strong><span style="color:#8e44ad;">Mutually Exclusive Sets</span></strong> are two sets that share NOTHING in common. </p>
<p><strong><span style="color:#e74c3c;">Example</span></strong></p>
<p>Imagine we have the two sets below. Recall that sets can be infinite.</p>
<p style="text-align: center;">Set $A =$ the set of all odd integers</p>
<p style="text-align: center;">Set $B = $ the set of all even integers</p>
<p><strong><span style="color:#27ae60;">What do they share in common? </span></strong></p>
<p>Nothing. They share nothing in common.</p>
<p><strong><span style="color:#27ae60;">What would their intersection be?</span></strong></p>
<p>The intersection of two mutually exclusive sets is what is known as the <strong><u>Null Set</u></strong> or the <strong><u>Empty Set</u></strong>. This means a set with nothing inside of it. And yes, that IS a valid set.</p>
<p><strong><span style="color:#27ae60;">What is the notation?</span></strong></p>
<p>$$null \ set = empty \ set = \{\varnothing\}$$</p>