Let U be a universal set with n(U) = 60. If n(A) = 32, n(B) = 27, and n(A ∩ B) = 11, what is n((A ∪ B)′), the number of elements in the complement of A ∪ B?
Answer and explanation
Correct answer: 12
First calculate the number of elements in A ∪ B. Because the 11 elements in A ∩ B are included in both A and B, they would be counted twice in n(A) + n(B), so subtract them once: n(A ∪ B) = 32 + 27 − 11 = 48. The complement (A ∪ B)′ contains all elements of U that are not in the union. Therefore, n((A ∪ B)′) = n(U) − n(A ∪ B) = 60 − 48 = 12. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
First calculate the number of elements in A ∪ B. Because the 11 elements in A ∩ B are included in both A and B, they would be counted twice in n(A) + n(B), so subtract them once: n(A ∪ B) = 32 + 27 − 11 = 48. The complement (A ∪ B)′ contains all elements of U that are not in the union. Therefore, n((A ∪ B)′) = n(U) − n(A ∪ B) = 60 − 48 = 12. Thus, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
