If n(A ∪ B) = 84 and n(A ∩ B) = 27, what is n(A − B) + n(B − A)?
Answer and explanation
Correct answer: 57
A union B 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). Substituting the given values gives 84 = n(A − B) + n(B − A) + 27. Rearranging, the requested sum is 84 − 27 = 57. This is also the size of the symmetric difference, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
57
Why is this the correct answer?
A union B 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). Substituting the given values gives 84 = n(A − B) + n(B − A) + 27. Rearranging, the requested sum is 84 − 27 = 57. This is also the size 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).
