If (A ∪ B)' = ∅ and A ∩ B = ∅, then B is equal to what?
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Answer and explanation
Correct answer: A'
The condition (A ∪ B)' = ∅ means that A ∪ B = U, because the only set whose complement is empty is the universal set itself. The condition A ∩ B = ∅ says that A and B are disjoint. Thus A and B partition U, so every element outside A must belong to B. Hence B = A'.
Frequently asked questions
What is the correct answer to this question?
A'
Why is this the correct answer?
The condition (A ∪ B)' = ∅ means that A ∪ B = U, because the only set whose complement is empty is the universal set itself. The condition A ∩ B = ∅ says that A and B are disjoint. Thus A and B partition U, so every element outside A must belong to B. Hence 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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