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.

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.
Given
n(A)=25, n(B)=26, and n(C)=26
n(A∩C)=9, n(A∩B)=11, and (B∩C)=8
n(A∩B∩C)=3
Let U be the set of people who took part in the survey
(i) 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 newspaper
(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 newspaper T and I only.
Let d denote the number of people who read all three newspaper.
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 + 3 = 28
⇒ a + b + c = 25
Hence, (52 - 25) = 30 people read exactly one newspaper.