Q. 154.1( 92 Votes )
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.
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 the 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 the number of people who read at least one of the newspaper
∴ 
= 25 + 26 + 26 – 11 – 8 – 9 + 3
= 80 – 28
= 52
∴ There are a total of 52 students who read at least 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
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