n(A ∪ B)= n(A)+ n(B)- n(A ∩ B)
Practical Problems on Union and Intersection of Three Sets
n(A ∪ B ∪ C)= n(A) +n(B)+ n(C)- n(A ∩ B)- n(B ∩ C)- n(C ∩ A)+ n(A ∩ B ∩ C)
Shaalaa.com | Practical Problems on Union and Intersection of Sets
In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
If X and Y are two sets such that X has 40 elements, X ∪Y has 60 elements and X ∩Y has 10 elements, how many elements does Y have?
In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?
In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I,11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
(i) the number of people who read at least one of the newspapers.
(ii) the number of people who read exactly one newspaper.
An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee; 25 students take milk and tea; 12 students take milk only; 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of three drinks is