If n(U) = 105 and n(A ∩ B) = 37, what is n((A ∩ B)ᶜ)?
Advertisement
Answer and explanation
Correct answer: 68
The complement of A ∩ B contains every element of the universal set U that is not in the intersection. For a finite universal set, the complement rule is n(Xᶜ) = n(U) − n(X). Taking X = A ∩ B gives n((A ∩ B)ᶜ) = 105 − 37 = 68. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
68
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 a finite universal set, the complement rule is n(Xᶜ) = n(U) − n(X). Taking X = A ∩ B gives n((A ∩ B)ᶜ) = 105 − 37 = 68. Hence option A is correct.
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.
Advertisement