If n(A union B) = 97, n(A) = 63, and n(B − A) = 34, which conclusion about n(A intersection B) is correct?
Answer and explanation
Correct answer: n(A intersection B) निर्धारित नहीं किया जा सकता
The union A union B is partitioned into three disjoint regions: A − B, A intersection B, and B − A. The given values provide n(A) = n(A − B) + n(A intersection B) = 63, while n(A union B) = n(A) + n(B − A) = 63 + 34 = 97. These equations are consistent for many intersection values, provided the corresponding A − B value changes. For example, an intersection of 10 gives A − B = 53, while an intersection of 20 gives A − B = 43. Hence the intersection cannot be determined uniquely; option D is correct.
Frequently asked questions
What is the correct answer to this question?
n(A intersection B) निर्धारित नहीं किया जा सकता
Why is this the correct answer?
The union A union B is partitioned into three disjoint regions: A − B, A intersection B, and B − A. The given values provide n(A) = n(A − B) + n(A intersection B) = 63, while n(A union B) = n(A) + n(B − A) = 63 + 34 = 97. These equations are consistent for many intersection values, provided the corresponding A − B value changes. For example, an intersection of 10 gives A − B = 53, while an intersection of 20 gives A − B = 43. Hence the intersection cannot be determined uniquely; option D 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).
