Question

In a survey of 100 persons, it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B and C and 3 read all the three magazines. Find: How many read none of three magazines?

Answer 1

Total number of People n(P) = 100. 

People who Read Magazine A n(A) =28. 

People who Read Magazine B n(B) = 30. 

People who Read Magazine C n(C) = 42. 

People who Read Magazine A and B n(A ∩ B) = 8 

People who Read Magazine B and C n(B ∩ C) = 10 

People who v Read Magazine A and C n(A ∩ C) = 5 

n(A∩B∩C)= 3 

Now, 

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

= 28+30+42–8–10–5+3 

= 100–20 

= 80 

People who read none of the three magazines 

= n(A∪B∪C)’

 = n(P) – n(A∪B∪C) 

= 100 –80 

= 20.

 ∴ People who read no magazine = 20