Answer
Venn diagram
Work Step by Step
(a)
The number of students who used only public transportation is represented by region VII:
\[\begin{align}
& \text{Number of students who used public transportation}=n\left( \text{VII} \right) \\
& =50
\end{align}\]
(b)
The number of students who usedboth cars and public transportation but not bikes is represented by region VI:
\[\begin{align}
& \text{Number of students who used both cars and public transport but not bikes}=n\left( \text{VI} \right) \\
& =26
\end{align}\]
(c)
The number of students who used cars or public transportation but not bikes is represented by sum of the regions V, VI, and VII:
\[\begin{align}
& \text{Number of students who used cars or public transportation but not bikes}=n\left( \text{V} \right)+n\left( \text{VI} \right)+n\left( \text{VII} \right) \\
& =54+26+50 \\
& =130
\end{align}\]
(d)
The number of students who used exactly two of these modes of transportation is represented by the sum of the regions II, IV, and VI:
\[\begin{align}
& \text{Number of students who used exactly two modes of transportation}=n\left( \text{II} \right)+n\left( \text{IV} \right)+n\left( \text{VI} \right) \\
& =16+4+26 \\
& =46
\end{align}\]
(e)
The number of students who did not use any of the three modes is represented by region VIII:
\[\begin{align}
& \text{Number of students who did not use any of the three modes}=n\left( \text{VII} \right) \\
& =0
\end{align}\]
