In a Venn diagram, n(U) = 85, n(A) = 42, n(B) = 36, and n(A ∩ B) = 14. How many elements are in neither set?
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Answer and explanation
Correct answer: 21
First calculate the union: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 42 + 36 − 14 = 64. The elements in neither A nor B form the complement of A ∪ B in the universal set U. Hence their number is n(U) − n(A ∪ B) = 85 − 64 = 21. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
First calculate the union: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 42 + 36 − 14 = 64. The elements in neither A nor B form the complement of A ∪ B in the universal set U. Hence their number is n(U) − n(A ∪ B) = 85 − 64 = 21. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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