If n(A) = 18, n(B) = 14, and n(A ∩ B) = 6, what is n(A ∪ B)?
Answer and explanation
Correct answer: 26
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is counted in both n(A) and n(B), so it must be subtracted once to correct the double count. Substituting the given values gives 18 + 14 − 6 = 26. Hence n(A ∪ B) = 26, so option A is correct. Option B forgets the overlap, while the other values result from incorrect arithmetic or sign usage.
Frequently asked questions
What is the correct answer to this question?
26
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). The intersection is counted in both n(A) and n(B), so it must be subtracted once to correct the double count. Substituting the given values gives 18 + 14 − 6 = 26. Hence n(A ∪ B) = 26, so option A is correct. Option B forgets the overlap, while the other values result from incorrect arithmetic or sign usage.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
