Question

In a survey of 100 families, the number of families that read the most recent
issues of various magazines was found to be: India Today 42. Sunday 30, New
Delhi 28, India Today and Sunday 10. India Today and New Delhi S. Sunday
and New Delhi 8, all three magazines 3, then the number of families that read
none of the three magazines is
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Answer 1

Answer:

Total number of persons=100

Number of persons who read magazine A=n(A)=28

Number of persons who read magazine B=n(B)=30

Number of persons who read magazine C=n(C)=42

Number of people who read both magazine A and B = n(A∩B)=8

Number of people who read both magazine B and C= n(B∩C)=5

Number of people who read both magazine A and C = n(A∩B)=10

Number of people who read both magazine A, B and C = n(A∩B∩C)=3

Number of people who read none of the three magazines= n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

n(A∪B∪C)=28+30+42−8−5−10+3

Therefore total number of readers=80

Number of readers who read none of the three magazines= 100−80=20