If n(U) = 32 and n(A ∩ B) = 9, how many elements are in (A ∩ B)'?
Answer and explanation
Correct answer: 23
The complement of A ∩ B contains every element of the universal set except the elements common to A and B. Therefore, use the complement formula n((A ∩ B)') = n(U) − n(A ∩ B). With the given values, the result is 32 − 9 = 23. Hence, option B is correct. The intersection itself has 9 elements, while its complement has the remaining 23.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
The complement of A ∩ B contains every element of the universal set except the elements common to A and B. Therefore, use the complement formula n((A ∩ B)') = n(U) − n(A ∩ B). With the given values, the result is 32 − 9 = 23. Hence, option B is correct. The intersection itself has 9 elements, while its complement has the remaining 23.
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.
