If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4, 5}, and B = {4, 5, 6, 7}, what is (A ∪ B)′?
Answer and explanation
Correct answer: {8, 9}
The relevant rule is that the complement of a set contains precisely the elements of U that are not in that set. Combining A and B gives A ∪ B = {1, 2, 3, 4, 5, 6, 7}; repeated elements 4 and 5 are written only once. Comparing this union with U = {1, ..., 9}, the missing elements are 8 and 9. Thus (A ∪ B)′ = {8, 9}. Option B is A without B, and option D is the common part.
Frequently asked questions
What is the correct answer to this question?
{8, 9}
Why is this the correct answer?
The relevant rule is that the complement of a set contains precisely the elements of U that are not in that set. Combining A and B gives A ∪ B = {1, 2, 3, 4, 5, 6, 7}; repeated elements 4 and 5 are written only once. Comparing this union with U = {1, ..., 9}, the missing elements are 8 and 9. Thus (A ∪ B)′ = {8, 9}. Option B is A without B, and option D is the common part.
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.
