If n(A) = 58, n(B) = 44, and n(A − B) = 23, what is n(A ∪ B)?
Advertisement
Answer and explanation
Correct answer: 67
The set A contains its exclusive part A − B and its common part A ∩ B. Therefore n(A ∩ B) = n(A) − n(A − B) = 58 − 23 = 35. Using the union formula, n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 58 + 44 − 35 = 67. The common elements must be subtracted once because they were counted twice.
Frequently asked questions
What is the correct answer to this question?
67
Why is this the correct answer?
The set A contains its exclusive part A − B and its common part A ∩ B. Therefore n(A ∩ B) = n(A) − n(A − B) = 58 − 23 = 35. Using the union formula, n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 58 + 44 − 35 = 67. The common elements must be subtracted once because they were counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
Advertisement