Answer
given below
Work Step by Step
(a)
In the Venn diagram, the region I represents the students who got the news only from newspapers. So, the required number of students is
\[\begin{align}
& n\left( \text{only newspapers} \right)=n\left( \text{I} \right) \\
& =22
\end{align}\]
(b)
In the Venn diagram, the region III represents the students who got the news only from television. So, the required number of students is
\[\begin{align}
& n\left( \text{only television} \right)=n\left( \text{III} \right) \\
& =36
\end{align}\]
(c)
In the Venn diagram, the sum of the regions I, II, and III represents the number of students who got the news from newspapers or television. So, the required number of students is
\[\begin{align}
& n\left( \text{newspapers or television} \right)=n\left( \text{I} \right)+n\left( \text{II} \right)+n\left( \text{III} \right) \\
& =22+7+36 \\
& =65
\end{align}\]
(d)
In the Venn diagram, the region IV represents the number of students who did not get the news from either newspapers or television. So, the required number of students is
\[\begin{align}
& n\left( \text{none} \right)=n\left( \text{IV} \right) \\
& =10
\end{align}\]
