If A ∩ B = ∅ and A ∪ B = U, then B is equal to what?
Answer and explanation
Correct answer: Aᶜ
The complement Aᶜ of A in the universal set U is the set of all elements of U that are not in A. The condition A ∩ B = ∅ says that A and B have no common elements, while A ∪ B = U says that together they contain every element of U. Thus B contains exactly those elements of U that are outside A. Therefore, B = Aᶜ, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Aᶜ
Why is this the correct answer?
The complement Aᶜ of A in the universal set U is the set of all elements of U that are not in A. The condition A ∩ B = ∅ says that A and B have no common elements, while A ∪ B = U says that together they contain every element of U. Thus B contains exactly those elements of U that are outside A. Therefore, B = Aᶜ, so option A 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.
