If n(U) = 100, n(A) = 52, and n(B) = 47, what is the minimum possible value of n(A ∩ B)?
Answer and explanation
Correct answer: 0
For two subsets of a universal set, the minimum possible intersection is max(0, n(A) + n(B) − n(U)). Here, 52 + 47 − 100 = −1, so the maximum with zero is 0. This is possible because the two sets together contain only 99 memberships, which can fit within the 100-element universal set without any overlap. Hence n(A ∩ B) can be 0.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
For two subsets of a universal set, the minimum possible intersection is max(0, n(A) + n(B) − n(U)). Here, 52 + 47 − 100 = −1, so the maximum with zero is 0. This is possible because the two sets together contain only 99 memberships, which can fit within the 100-element universal set without any overlap. Hence n(A ∩ B) can be 0.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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