If A ∪ B = U and A ∩ B = ∅, what is B equal to?
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Answer and explanation
Correct answer: A′
The condition A ∪ B = U says that together the two sets contain every element of the universal set. The condition A ∩ B = ∅ says that they have no common element. Therefore, every element outside A must belong to B, and every element outside B must belong to A. Hence B is exactly the complement of A, so B = A′.
Frequently asked questions
What is the correct answer to this question?
A′
Why is this the correct answer?
The condition A ∪ B = U says that together the two sets contain every element of the universal set. The condition A ∩ B = ∅ says that they have no common element. Therefore, every element outside A must belong to B, and every element outside B must belong to A. Hence B is exactly the complement of A, so B = A′.
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.
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