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$n(H\cap T\cap I)=3$
$\therefore n(H\cup T\cup I)=n(H)+n(T)+n(I)-n(H\cap I)$
$-n(H\cap T)-n(T\cap I)+n(H\cap T\cap I)$
$=25+26+26-9-11-8+3$
$=80-28=52$