If n(A) = 14, n(B) = 10, and n(A ∩ B) = 3, what is n(A ∪ B)?
Answer and explanation
Correct answer: 21
For two finite sets, the inclusion-exclusion principle states n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Adding 14 and 10 counts each of the three common elements twice, so one copy of the intersection must be subtracted. Therefore, n(A ∪ B) = 14 + 10 − 3 = 21. Option B is correct; 24 fails to remove overlap, while 17 and 27 use incorrect arithmetic or operations.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
For two finite sets, the inclusion-exclusion principle states n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Adding 14 and 10 counts each of the three common elements twice, so one copy of the intersection must be subtracted. Therefore, n(A ∪ B) = 14 + 10 − 3 = 21. Option B is correct; 24 fails to remove overlap, while 17 and 27 use incorrect arithmetic or operations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
