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Out of 100 people, 40 read newspaper A, 30 read newspaper B, and 10 read both. How many read neither?
30
40
50
60
40
Subtract the intersection from the sum of individual sets to find the union (40+30тИТ10=60), then subtract this union from the total population (100тИТ60=40).
Total population = 100, Newspaper A readers = 40, Newspaper B readers = 30, Readers of both = 10.
n(AтИкB)=n(A)+n(B)тИТn(AтИйB)
Subtract the intersection from the sum of individual sets to find the union (40+30тИТ10=60), then subtract this union from the total population (100тИТ60=40).
Students often add 40 and 30 to get 70 and then subtract from 100, forgetting to subtract the 10 who were counted twice in the intersection.
Calculate Union of Sets
Use the inclusion-exclusion principle to find the number of people reading at least one newspaper, which is n(AтИкB).
n(AтИкB)=40+30тИТ10=60
Calculate Neither
Subtract the number of people who read at least one newspaper from the total population to find those who read neither.
Neither=TotalтИТn(AтИкB)=100тИТ60=40
B is correct because the number of people who read neither is 40, calculated by subtracting the union of sets from the total population.
This principle is the foundation for solving complex data interpretation questions in banking and CAT exams involving overlapping survey data sets.