If (A ∩ B)′ = A′ ∩ B′ holds in a universal set U, what can be said about A and B?
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Answer and explanation
Correct answer: A ∪ B = A ∩ B
De Morgan’s law always gives (A ∩ B)′ = A′ ∪ B′. The stated equality therefore requires A′ ∪ B′ = A′ ∩ B′. For two sets, a union equals their intersection exactly when the two sets are equal, so A′ = B′. Taking complements on both sides gives A = B. Consequently, A ∪ B = A ∩ B, which is option A.
Frequently asked questions
What is the correct answer to this question?
A ∪ B = A ∩ B
Why is this the correct answer?
De Morgan’s law always gives (A ∩ B)′ = A′ ∪ B′. The stated equality therefore requires A′ ∪ B′ = A′ ∩ B′. For two sets, a union equals their intersection exactly when the two sets are equal, so A′ = B′. Taking complements on both sides gives A = B. Consequently, A ∪ B = A ∩ B, which is option 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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