If n(A ∪ B) = 98 and n(A ∩ B) = 35, what is the value of n(A − B) + n(B − A)?
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Answer and explanation
Correct answer: 63
The union is partitioned into three disjoint regions: A − B, A ∩ B, and B − A. Therefore, n(A ∪ B) = n(A − B) + n(A ∩ B) + n(B − A). Substituting the given values gives n(A − B) + n(B − A) = 98 − 35 = 63. This is also the cardinality of the symmetric difference, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
63
Why is this the correct answer?
The union is partitioned into three disjoint regions: A − B, A ∩ B, and B − A. Therefore, n(A ∪ B) = n(A − B) + n(A ∩ B) + n(B − A). Substituting the given values gives n(A − B) + n(B − A) = 98 − 35 = 63. This is also the cardinality of the symmetric difference, so option A is correct.
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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