<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-complete-overlap" target="_blank">Complete Overlap Exercise</a></p><p>It's also possible for two sets to have <strong><span style="color:#8e44ad;">Complete Overlap</span></strong>.</p>
<p><strong><span style="color:#27ae60;">Case 1: The two sets are identical.</span></strong></p>
<p style="margin-left: 40px;"><strong><u>Implication</u></strong>: Both the intersection and the union of the two sets are equal to each set individually.</p>
<p>$$A \cap B = Set \ A = Set \ B = A \cup B$$</p>
<p style="margin-left: 40px;"><strong><span style="color:#e74c3c;">Example</span></strong></p>
<p style="margin-left: 40px;">What is the overlap between Set $A$, $\{1, 2, 3 \}$ and Set $B$, $\{1, 2, 3\}$. In this case, it's equal to both sets individually.</p>
<p>$$A \cap B = \{1, 2, 3 \} = \{1, 2, 3 \} = A \cup B$$</p>
<p><strong><span style="color:#27ae60;">Case 2: The set with fewer elements is contained entirely in the larger set.</span></strong></p>
<p style="margin-left: 40px;"><strong><u>Implication</u></strong>: The intersection of the two sets is equal to the smaller set. The union of the two sets is equal to the larger set.</p>
<p style="text-align: center;">$A \cap B =$ set with fewer elements</p>
<p style="text-align: center;">$A \cup B = $ set with more elements</p>
<p style="margin-left: 40px;"><strong><span style="color:#e74c3c;">Example</span></strong></p>
<p style="margin-left: 40px;">What is the overlap between Set $A$, all prime numbers, and Set $B$, all integers? </p>
<p style="margin-left: 40px;">Well, all prime numbers are integers, but not all integers are prime numbers.</p>
<p style="text-align: center;">$A \cap B =$ $\{$all prime numbers$\}$</p>
<p style="text-align: center;">$A \cup B =$ $\{$all integers$\}$</p>