If n(U) = 120, n(A) = 77, and n(B) = 64, what is the minimum possible value of n(A ∩ B)?
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Answer and explanation
Correct answer: 21
The total of the two set sizes is 77 + 64 = 141, which is 21 greater than the 120 elements available in U. Those extra 21 memberships must occur in the overlap. Using the lower-bound formula, n(A ∩ B) ≥ n(A) + n(B) − n(U), the minimum is 77 + 64 − 120 = 21. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
The total of the two set sizes is 77 + 64 = 141, which is 21 greater than the 120 elements available in U. Those extra 21 memberships must occur in the overlap. Using the lower-bound formula, n(A ∩ B) ≥ n(A) + n(B) − n(U), the minimum is 77 + 64 − 120 = 21. Thus option C 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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