If n(U) = 100, n(A) = 64, and n(B) = 58, what is the minimum possible value of n(A ∪ B)?
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Answer and explanation
Correct answer: 64
The union A ∪ B must contain every element of A and every element of B, so its size cannot be less than either set. Therefore n(A ∪ B) ≥ max(64, 58) = 64. This minimum is attainable because B, which has 58 elements, can be completely contained in A, which has 64 elements. Thus n(A ∪ B) = 64.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The union A ∪ B must contain every element of A and every element of B, so its size cannot be less than either set. Therefore n(A ∪ B) ≥ max(64, 58) = 64. This minimum is attainable because B, which has 58 elements, can be completely contained in A, which has 64 elements. Thus n(A ∪ B) = 64.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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