If n(A \ B) = 12, n(A ∩ B) = 7, and n(B \ A) = 16, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 35
The union A ∪ B contains three mutually disjoint regions: the elements only in A, the elements common to A and B, and the elements only in B. Hence n(A ∪ B) = 12 + 7 + 16 = 35. Option B omits the common region, while option C is only 12 + 7. Option D has no valid interpretation for the given partition.
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
The union A ∪ B contains three mutually disjoint regions: the elements only in A, the elements common to A and B, and the elements only in B. Hence n(A ∪ B) = 12 + 7 + 16 = 35. Option B omits the common region, while option C is only 12 + 7. Option D has no valid interpretation for the given partition.
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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