If n(A union B) = 92, n(A − B) = 35, and n(A intersection B) = 24, what is n(B − A)?
Answer and explanation
Correct answer: 33
The union of two sets consists of three disjoint Venn-diagram regions: A − B, A intersection B, and B − A. Thus n(A union B) = n(A − B) + n(A intersection B) + n(B − A). Substitution gives 92 = 35 + 24 + n(B − A). Solving, n(B − A) = 92 − 35 − 24 = 33. The value 59 is only 35 + 24 and does not represent the missing B-only region. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The union of two sets consists of three disjoint Venn-diagram regions: A − B, A intersection B, and B − A. Thus n(A union B) = n(A − B) + n(A intersection B) + n(B − A). Substitution gives 92 = 35 + 24 + n(B − A). Solving, n(B − A) = 92 − 35 − 24 = 33. The value 59 is only 35 + 24 and does not represent the missing B-only region. Hence 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).
