Question

In a survey of 60 people, it was found that 25 people read N magazine, 26 read T magazine and 26 read F magazine. Also 9 read both N & F, 11 read both N & T, 8 read both T & F, 8 read no magazine at all:

i) Find number of people who read all 3 magazines.
ii) Determine the number of people who read exactly one magazine.
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Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Let A be the set of people who read magazine N.

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

Let C be the set of people who read magazine F.

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 magazine N and T only.

Let b denote the number of people who read magazine F and N only.

Let c denote the number of people who read magazine T and F only.

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

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 magazine.