If n(U) = 75, n(A) = 42, n(B) = 38, and n(A ∩ B) = 20, what is n((A ∪ B)ᶜ)?
Answer and explanation
Correct answer: 15
First use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 42 + 38 − 20 = 60. The complement of A ∪ B contains the elements of U that are not in either A or B. Therefore, n((A ∪ B)ᶜ) = n(U) − n(A ∪ B) = 75 − 60 = 15. Thus option A is correct. The value 60 represents the union, not its complement.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
First use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 42 + 38 − 20 = 60. The complement of A ∪ B contains the elements of U that are not in either A or B. Therefore, n((A ∪ B)ᶜ) = n(U) − n(A ∪ B) = 75 − 60 = 15. Thus option A is correct. The value 60 represents the union, 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.
