If n(A ∪ B ∪ C) = 88, n(A − B) = 19, n(B − A) = 24, n(A ∩ B) = 13, and C − (A ∪ B) has 32 elements, what is n((A ∪ B) − C) if C has no element of A ∪ B?
Answer and explanation
Correct answer: 56
The sets C and A ∪ B are disjoint by the condition that C contains no element of A ∪ B. Hence removing C from A ∪ B does not change A ∪ B, so (A ∪ B) − C = A ∪ B. The union A ∪ B consists of A − B, B − A, and A ∩ B, which are disjoint parts. Therefore its cardinality is 19 + 24 + 13 = 56. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
56
Why is this the correct answer?
The sets C and A ∪ B are disjoint by the condition that C contains no element of A ∪ B. Hence removing C from A ∪ B does not change A ∪ B, so (A ∪ B) − C = A ∪ B. The union A ∪ B consists of A − B, B − A, and A ∩ B, which are disjoint parts. Therefore its cardinality is 19 + 24 + 13 = 56. 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).
