If A, B and C are mutually disjoint, n(A)=27, n(B)=34, n(C)=41 and n(U)=125, what is n((A∪B∪C)′)?
Answer and explanation
Correct answer: 23
Mutually disjoint sets have no common elements, so their union has size equal to the sum of their sizes: n(A∪B∪C)=27+34+41=102. The complement of this union contains the elements of U outside all three sets. Using n(X′)=n(U)−n(X), we get 125−102=23. Thus option A is correct; 102 is the union size, not its complement.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Mutually disjoint sets have no common elements, so their union has size equal to the sum of their sizes: n(A∪B∪C)=27+34+41=102. The complement of this union contains the elements of U outside all three sets. Using n(X′)=n(U)−n(X), we get 125−102=23. Thus option A is correct; 102 is the union size, not its complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
