If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 3}, and B = {4, 5}, how many elements are in (A ∪ B)′?
Answer and explanation
Correct answer: 3
First find the union of A and B: A ∪ B = {1, 2, 3, 4, 5}. The complement is always taken with respect to the universal set U, so (A ∪ B)′ = U \ (A ∪ B) = {6, 7, 8}. This set contains 3 elements, giving option A. Equivalently, because U has 8 elements and the union has 5 elements, its complement has 8 − 5 = 3 elements.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
First find the union of A and B: A ∪ B = {1, 2, 3, 4, 5}. The complement is always taken with respect to the universal set U, so (A ∪ B)′ = U \ (A ∪ B) = {6, 7, 8}. This set contains 3 elements, giving option A. Equivalently, because U has 8 elements and the union has 5 elements, its complement has 8 − 5 = 3 elements.
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.
