If n(A ∪ B) = 88, n(A ∩ B) = 26, and n(A − B) = 35, what is n(B)?
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Answer and explanation
Correct answer: 53
First split set A into the disjoint regions A − B and A ∩ B. Thus n(A) = 35 + 26 = 61. Now use n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the known values gives 88 = 61 + n(B) − 26, so n(B) = 53. Option B is n(A), not n(B), making option A the correct answer.
Frequently asked questions
What is the correct answer to this question?
53
Why is this the correct answer?
First split set A into the disjoint regions A − B and A ∩ B. Thus n(A) = 35 + 26 = 61. Now use n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the known values gives 88 = 61 + n(B) − 26, so n(B) = 53. Option B is n(A), not n(B), making option A the correct answer.
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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