If n(U) = 50, n(A) = 20, n(B) = 16, and n(A ∩ B) = 6, how many elements are in neither A nor B?
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Answer and explanation
Correct answer: 20
First find the union using inclusion–exclusion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 20 + 16 − 6 = 30. The elements in neither A nor B form the complement of A ∪ B in U. Therefore, their number is n(U) − n(A ∪ B) = 50 − 30 = 20. Hence, option B is correct; 30 is the union, not the neither region.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
First find the union using inclusion–exclusion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 20 + 16 − 6 = 30. The elements in neither A nor B form the complement of A ∪ B in U. Therefore, their number is n(U) − n(A ∪ B) = 50 − 30 = 20. Hence, option B is correct; 30 is the union, not the neither region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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