If A' ∩ B' = U, what is the correct conclusion about A ∪ B?
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Answer and explanation
Correct answer: A ∪ B = ∅
By De Morgan’s law, A' ∩ B' = (A ∪ B)'. The given condition therefore says that the complement of A ∪ B is the entire universal set U. The only set whose complement is U is the empty set, because ∅' = U. Taking complements on both sides also gives A ∪ B = ∅. Thus option A is the only correct conclusion.
Frequently asked questions
What is the correct answer to this question?
A ∪ B = ∅
Why is this the correct answer?
By De Morgan’s law, A' ∩ B' = (A ∪ B)'. The given condition therefore says that the complement of A ∪ B is the entire universal set U. The only set whose complement is U is the empty set, because ∅' = U. Taking complements on both sides also gives A ∪ B = ∅. Thus option A is the only correct conclusion.
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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