If n(U) = 90 and n(A ∩ B) = 25, what is n((A ∩ B)′)?
Answer and explanation
Correct answer: 65
The governing concept is the cardinality of a complement in a finite universal set. For any subset X of U, n(X′) = n(U) − n(X), because the universal set is divided into X and the elements outside X. Taking X = A ∩ B gives n((A ∩ B)′) = 90 − 25 = 65. Option B is correct; 25 is the original intersection, 90 ignores the excluded part, and 115 exceeds the universal-set size.
Frequently asked questions
What is the correct answer to this question?
65
Why is this the correct answer?
The governing concept is the cardinality of a complement in a finite universal set. For any subset X of U, n(X′) = n(U) − n(X), because the universal set is divided into X and the elements outside X. Taking X = A ∩ B gives n((A ∩ B)′) = 90 − 25 = 65. Option B is correct; 25 is the original intersection, 90 ignores the excluded part, and 115 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.
