If n(U) = 92 and n(A ∪ B) = 67, how many elements are in the region that is neither in A nor in B in the Venn diagram?
Answer and explanation
Correct answer: 25
The region containing elements that are neither in A nor in B is the complement of their union, written as (A ∪ B)′. The universal set contains 92 elements, while the union contains 67 elements. Therefore the outside region has n((A ∪ B)′) = n(U) − n(A ∪ B) = 92 − 67 = 25 elements. Thus option A is correct. The value 67 represents the union itself, not the region outside both sets.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The region containing elements that are neither in A nor in B is the complement of their union, written as (A ∪ B)′. The universal set contains 92 elements, while the union contains 67 elements. Therefore the outside region has n((A ∪ B)′) = n(U) − n(A ∪ B) = 92 − 67 = 25 elements. Thus option A is correct. The value 67 represents the union itself, not the region outside both sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
