If n(U) = 60, n(A) = 35, and n(B) = 32, what is the minimum possible value of n(A ∩ B)?
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Answer and explanation
Correct answer: 7
For two subsets of a universal set, n(A ∪ B) cannot exceed n(U). Using n(A ∪ B) = n(A) + n(B) − n(A ∩ B), we require 60 ≥ 35 + 32 − n(A ∩ B). Hence n(A ∩ B) ≥ 7. This bound is attainable when the union contains all 60 elements, so the minimum possible intersection is 7.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For two subsets of a universal set, n(A ∪ B) cannot exceed n(U). Using n(A ∪ B) = n(A) + n(B) − n(A ∩ B), we require 60 ≥ 35 + 32 − n(A ∩ B). Hence n(A ∩ B) ≥ 7. This bound is attainable when the union contains all 60 elements, so the minimum possible intersection is 7.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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