If n(U) = 180, n(A) = 109, and n(B) = 97, what is the minimum possible value of n(A ∪ B)?
Answer and explanation
Correct answer: 109
The union contains all elements of both sets, so it must contain at least as many elements as the larger set. Therefore n(A ∪ B) ≥ max(n(A), n(B)) = 109. This lower bound is attainable if the smaller set B is completely contained in A. In that case A ∪ B = A and its cardinality is 109. Hence the minimum possible value is 109, option A.
Frequently asked questions
What is the correct answer to this question?
109
Why is this the correct answer?
The union contains all elements of both sets, so it must contain at least as many elements as the larger set. Therefore n(A ∪ B) ≥ max(n(A), n(B)) = 109. This lower bound is attainable if the smaller set B is completely contained in A. In that case A ∪ B = A and its cardinality is 109. Hence the minimum possible value is 109, option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
