If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A ∪ B)'?
Answer and explanation
Correct answer: {6, 7, 8}
First find the union: A ∪ B = {1, 2, 3, 4, 5}. The complement is taken relative to the universal set U, so remove every element of this union from U. The remaining elements are {6, 7, 8}. Hence (A ∪ B)' = {6, 7, 8}. Option A gives the union itself, while option C incorrectly includes 1 and 2; therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
{6, 7, 8}
Why is this the correct answer?
First find the union: A ∪ B = {1, 2, 3, 4, 5}. The complement is taken relative to the universal set U, so remove every element of this union from U. The remaining elements are {6, 7, 8}. Hence (A ∪ B)' = {6, 7, 8}. Option A gives the union itself, while option C incorrectly includes 1 and 2; therefore option B is correct.
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.
