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Question

Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: $$ \begin{matrix} \text{} & \text{Freshmen} & \text{Sophomores}\\ \text{Arts & Sciences} & \text{19} & \text{14}\\ \text{Business} & \text{66} & \text{21}\\ \end{matrix} $$ Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B the set of students from the College of Business, F the set of freshmen, and S the set of sophomores. $n(A \cup S)$

Solution

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We know, AA is set of students from College of Art &\& Sciences and SS is set of Sophomores.

ASA \cup S represents set of students from College of Art &\& Sciences or are sophomores

Given, there are:

  • 19 freshmen in College of Art &\& Sciences
  • 14 sophomores in College of Art &\& Sciences
  • 21 sophomores in College of Business

Hence,

n(AS)=19+14+21=54\begin{align*} n(A \cup S)&=19+14+21\\ &=\textcolor{#4257b2}{54} \end{align*}

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