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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

VerifiedStep 1

1 of 2We know, $A$ is set of students from College of Art $\&$ Sciences and $S$ is set of Sophomores.

$A \cup S$ 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,

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

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