Let A be the set of people who read newspaper H.

Let B be the set of people who read newspaper T.

Let C be the set of people who read newspaper I.

Accordingly, n(A) = 25, n(B) = 26, and n(C) = 26

n(A ∩ C) = 9, n(A ∩ B) = 11, and n(B ∩ C) = 8

n(A ∩ B ∩ C) = 3

Let U be the set of people who took part in the survey.

(i) Accordingly,

n(A B C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

= 25 + 26 + 26 – 11 – 8 – 9 + 3

= 52

Hence, 52 people read at least one of the newspapers.

(ii) Let 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.

Let d denote the number of people who read all three newspapers.

Accordingly, d = n(A ∩ B ∩ C) = 3

Now, n(A ∩ B) = a + d

n(B ∩ C) = c + d

n(C ∩ A) = b + d

a + d + c + d + b + d = 11 + 8 + 9 = 28

a + b + c + d = 28 – 2d = 28 – 6 = 22

Hence, (52 – 22) = 30 people read exactly one newspaper

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1) n(H U T U I) = n(H) + n(T) + n(I) - n(H ∩ T) - n(T ∩ I) - n(I ∩ H) + n(H ∩ T ∩ I)

==> n(H U T U I) = 25 + 26 + 26 - 11 - 8 - 9 + 3 = 52

==> Total number of people read one or more papers is 52.

But given survey is done among 60 people; so 8 of them do not read any of the papers mentioned.

2) Only n(H U T) = n(H ∩ T) - n(H ∩ T ∩ I)

==> Only n(H U T) = 11 - 3 = 8

Similalry Only n(T U I) = 8 - 3 = 5

and Only n(I U H) = 9 - 3 = 6

3) Thus from the above, number of persons reading either two or three papers =

= Only n(H U T) + Only n(T U I) + Only n(I U H) + n(H ∩ T ∩ I) = 8 + 5 + 6 + 3 = 22

4) So number of people reading only one paper = Total number of people reading one or more papers - number reading two or three papers

= 52 - 22 = 30

Thus number of people reading only one paper = 30

Alternatively, you may try to solve in another method also:

i) Number of people read only H = Total H - (H ∩ T) - (H ∩ I) + (H ∩ T ∩ I)
= 25 - 11 - 9 + 3 = 8

ii) NUmber of people read only T = 26 - 11 - 8 + 3 = 10

iii) Number of people read only I = 26 - 8 - 9 + 3 = 12

So total reading only one paper = 8 + 10 + 12 = 30

However of the above two, the best one to solve is with VENN Diagram,

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thx u very much thx alot

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Thank you
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Hope this would help • 6 • 3
b) 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 the three newspapers. Using the Venn diagram answer the following questions: i) No. of people who read atleast one newspaper. (1) ii) No. of people who read the newspaper H only.

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