in survey of 60 people , it was found that 25 people read newspaper H , 26 read newpaper T , 26 read newspaper I , 9 read both H and I , 11 read both H and T , 8 read T and I , 3 read all these newspaper find
- the number of peoplewho read at least one of the new paper
- the number of people who read exactly one newpaper
- who read H but neither T nor I
- who read T and H but not I
plz replz as soon as possible , plz plz infinit
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