If n(A) = 45, n(B) = 38, and n(A ∪ B) = 63, find n(A ∩ B).
Answer and explanation
Correct answer: 20
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 63 = 45 + 38 − n(A ∩ B), or 63 = 83 − n(A ∩ B). Therefore n(A ∩ B) = 83 − 63 = 20. The overlap is subtracted because common elements are counted twice in n(A) + n(B), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 63 = 45 + 38 − n(A ∩ B), or 63 = 83 − n(A ∩ B). Therefore n(A ∩ B) = 83 − 63 = 20. The overlap is subtracted because common elements are counted twice in n(A) + n(B), 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).
