If n(A ∪ B) = 104, n(A − B) = 46, and n(A ∩ B) = 25, what is n(B − A)?
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Answer and explanation
Correct answer: 33
The union is partitioned into three disjoint regions: elements only in A, elements only in B, and elements in both sets. Thus, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substitution gives 104 = 46 + n(B − A) + 25, so n(B − A) = 33. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The union is partitioned into three disjoint regions: elements only in A, elements only in B, and elements in both sets. Thus, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substitution gives 104 = 46 + n(B − A) + 25, so n(B − A) = 33. 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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