If n(A) = 31, n(B) = 22, and n(A ∩ B) = 9, what is n(A ∪ B)?
Answer and explanation
Correct answer: 44
The governing rule is the two-set inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since the 9 common elements occur in both sets, direct addition would count them twice. Substitution gives n(A ∪ B) = 31 + 22 − 9 = 44. Hence option A is correct. Option B is the uncorrected sum, while the other values do not satisfy the formula.
Frequently asked questions
What is the correct answer to this question?
44
Why is this the correct answer?
The governing rule is the two-set inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since the 9 common elements occur in both sets, direct addition would count them twice. Substitution gives n(A ∪ B) = 31 + 22 − 9 = 44. Hence option A is correct. Option B is the uncorrected sum, while the other values do not satisfy the formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
