If n(A \ B) = 18, n(B \ A) = 14, and n(A ∩ B) = 9, what is n(A ∪ B)?
Answer and explanation
Correct answer: 41
The union is partitioned into three disjoint regions: elements only in A, counted by n(A \ B); elements only in B, counted by n(B \ A); and common elements, counted by n(A ∩ B). Therefore n(A ∪ B) = 18 + 14 + 9 = 41. The common part is added once only, so option C is correct. Options A and B omit a region, while D overcounts.
Frequently asked questions
What is the correct answer to this question?
41
Why is this the correct answer?
The union is partitioned into three disjoint regions: elements only in A, counted by n(A \ B); elements only in B, counted by n(B \ A); and common elements, counted by n(A ∩ B). Therefore n(A ∪ B) = 18 + 14 + 9 = 41. The common part is added once only, so option C is correct. Options A and B omit a region, while D overcounts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
