If n(U) = 150 and n(A ∪ B) = 118, what is the number of elements in (A ∪ B)ᶜ?
Advertisement
Answer and explanation
Correct answer: 32
The complement of A ∪ B contains the elements of the universal set U that do not belong to A ∪ B. A set and its complement partition the universal set, so n((A ∪ B)ᶜ) = n(U) − n(A ∪ B). Substitution gives 150 − 118 = 32. Therefore, option A is correct; 118 is the union’s size, not its complement.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The complement of A ∪ B contains the elements of the universal set U that do not belong to A ∪ B. A set and its complement partition the universal set, so n((A ∪ B)ᶜ) = n(U) − n(A ∪ B). Substitution gives 150 − 118 = 32. Therefore, option A is correct; 118 is the union’s size, not its complement.
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.
Advertisement