If n(U) = 96 and n(A ∩ B) = 34, what is n((A ∩ B)′)?
Answer and explanation
Correct answer: 62
The complement of A ∩ B contains every element of the universal set U that is not in the intersection. For any finite set X contained in U, n(X′) = n(U) − n(X). Taking X = A ∩ B gives n((A ∩ B)′) = 96 − 34 = 62. Therefore option B is correct. The value 34 is the intersection itself, while 130 cannot be a complement size because it exceeds the universal-set size.
Frequently asked questions
What is the correct answer to this question?
62
Why is this the correct answer?
The complement of A ∩ B contains every element of the universal set U that is not in the intersection. For any finite set X contained in U, n(X′) = n(U) − n(X). Taking X = A ∩ B gives n((A ∩ B)′) = 96 − 34 = 62. Therefore option B is correct. The value 34 is the intersection itself, while 130 cannot be a complement size because it exceeds the universal-set size.
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.
