If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, and B = {6, 7}, what is (A ∪ B)′?
Answer and explanation
Correct answer: {5, 8, 9}
First calculate the union: A ∪ B = {1, 2, 3, 4, 6, 7}. The complement is taken relative to U, so we remove every member of this union from U. The elements left are 5, 8, and 9. Thus, (A ∪ B)′ = {5, 8, 9}, which is option A. Option B is the union itself, while option C incorrectly includes 6 and 7, which are already in the union.
Frequently asked questions
What is the correct answer to this question?
{5, 8, 9}
Why is this the correct answer?
First calculate the union: A ∪ B = {1, 2, 3, 4, 6, 7}. The complement is taken relative to U, so we remove every member of this union from U. The elements left are 5, 8, and 9. Thus, (A ∪ B)′ = {5, 8, 9}, which is option A. Option B is the union itself, while option C incorrectly includes 6 and 7, which are already in the union.
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.
