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 both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
(i) The number of people who read at least one of the newspapers.

(ii) The number of people who read exactly one newspaper.

Question

Philoid · Accepted Answer

(i) Let us assume A be the set of people who read newspaper H

Also, let B be the set of people who read newspaper T

And, let C be the set of people who read newspaper I

It is given in the question that,

Number of people who read newspaper H, n (A) = 25

Number of people who read newspaper T, n (B) = 26

Number of people who read newspaper I, n (C) = 26

Number of people who read both newspaper H and I,

Number of people who read both newspaper H and T,

Number of people who read both newspaper T and I,

And, Number of people who read all three newspaper H, T and I,

Now, we have to find number of people who read atleast one of the newspaper

∴

= 25 + 26 + 26 – 11 – 8 – 9 + 3

= 80 – 28

= 52

∴ There are total 52 students who read atleast one newspaper

(ii) Let us assume a be the number of people who read newspapers H and T only

Let b denote the number of people who read newspapers I and H only

Let c denote the number of people who read newspapers T and I only

And, let d denote the number of people who read all three newspapers

It is given in the question that:

Now, we have:

And,

∴ a + d + c +d + b + d = 11 + 8 + 9

a + b + c + d = 28 – 2d

= 28 – 6

= 22

∴ Number of people read exactly one newspaper = 52 – 22

= 30 people