If n(U) = 160, n(A) = 92, and n(B) = 83, what is the minimum possible value of n(A ∩ B)?
Answer and explanation
Correct answer: 15
For two subsets of a universal set, the intersection must satisfy n(A ∩ B) ≥ n(A) + n(B) − n(U). This follows because the two sets together cannot contain more than the 160 elements of U. Here, the lower bound is 92 + 83 − 160 = 15. This value is attainable when the union is the entire universal set, so the minimum possible intersection is 15. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
For two subsets of a universal set, the intersection must satisfy n(A ∩ B) ≥ n(A) + n(B) − n(U). This follows because the two sets together cannot contain more than the 160 elements of U. Here, the lower bound is 92 + 83 − 160 = 15. This value is attainable when the union is the entire universal set, so the minimum possible intersection is 15. Option B is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
