If n(A) = 26, n(B) = 19, and n(A ∩ B) = 8, what is n(A ∪ B)?
Answer and explanation
Correct answer: 37
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 26 + 19 − 8 = 37. The intersection is subtracted because the eight common elements were counted once in n(A) and once again in n(B). Thus the union contains 37 elements, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
37
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 26 + 19 − 8 = 37. The intersection is subtracted because the eight common elements were counted once in n(A) and once again in n(B). Thus the union contains 37 elements, 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).
