If A ⊆ B ⊆ U, n(U) = 150, n(A) = 64, and n(B) = 97, what is n(A′ ∩ B)?
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Answer and explanation
Correct answer: 33
Because A is a subset of B, the elements in B that are outside A are exactly B − A. The set identity A′ ∩ B = B − A therefore applies. Removing the 64 elements of A from the 97 elements of B gives n(A′ ∩ B) = 97 − 64 = 33. The size of U is extra information and does not affect this difference.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
Because A is a subset of B, the elements in B that are outside A are exactly B − A. The set identity A′ ∩ B = B − A therefore applies. Removing the 64 elements of A from the 97 elements of B gives n(A′ ∩ B) = 97 − 64 = 33. The size of U is extra information and does not affect this difference.
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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