Question

In a survey of 60 people, it was found that 25 people read newspaper $H$, 26 read newspaper $T, 26$ read newspaper $I, 9$ read $H$ and $I, 11$ read $H$ and T, 8 read $T$ and $I, 3$ read all three newspapers.
The number of people who read atleast one of the newspaper, is

• A. 60
• B. 46
• C. 52
• D. 58

Answer 1

Answer: (C)

Let $H$ be the set of those people who read newspaper $H, T$ be the set of those people who read newspaper $T$ and $/$ be the set of those people who read newspaper $I$.
Then, $ n(H)=25, n(T)=26, n(I)=26$
$n(H \cap I)=9, n(H \cap T)=11, n(T \cap I)=8$
and$ n(H \cap T \cap I)=3 $
$ \therefore n(H \cup T \cup I)=n(H)+n(T)+n(I)-n(H \cap I)$
$ -n(H \cap T)-n(T \cap I)+n(H \cap T \cap I)$
$ =25+26+26-9-11-8+3$
$ =80-28=52 $