If A ⊆ B ⊆ U, n(U) = 90, n(B) = 54, and n(A) = 31, what is n(A′ ∩ B)?
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Answer and explanation
Correct answer: 23
The expression A′ ∩ B represents the elements that belong to B but do not belong to A. Since A is a subset of B, removing all 31 elements of A from the 54 elements of B leaves B − A. Therefore, n(A′ ∩ B) = n(B) − n(A) = 54 − 31 = 23. The value n(U) is not needed for this calculation.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
The expression A′ ∩ B represents the elements that belong to B but do not belong to A. Since A is a subset of B, removing all 31 elements of A from the 54 elements of B leaves B − A. Therefore, n(A′ ∩ B) = n(B) − n(A) = 54 − 31 = 23. The value n(U) is not needed for this calculation.
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.
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