If n(U) = 150, n(A) = 91, and n(B) = 86, what is the minimum possible value of n(A ∪ B)?
Answer and explanation
Correct answer: 91
A union contains every element of each participating set, so it must contain the larger set. Therefore, n(A ∪ B) ≥ max[n(A), n(B)] = max(91, 86) = 91. This lower bound is possible if all 86 elements of B lie inside A, meaning B ⊆ A. Then A ∪ B = A and has 91 elements. Option B is too small, while 177 is the sum without accounting for overlap.
Frequently asked questions
What is the correct answer to this question?
91
Why is this the correct answer?
A union contains every element of each participating set, so it must contain the larger set. Therefore, n(A ∪ B) ≥ max[n(A), n(B)] = max(91, 86) = 91. This lower bound is possible if all 86 elements of B lie inside A, meaning B ⊆ A. Then A ∪ B = A and has 91 elements. Option B is too small, while 177 is the sum without accounting for overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
