If A and B are subsets of U, what is (A ∪ B)′ equal to?
Answer and explanation
Correct answer: A′ ∩ B′
De Morgan’s law states that the complement of a union equals the intersection of the complements: (A ∪ B)′ = A′ ∩ B′. An element lies outside A ∪ B only when it belongs to neither A nor B. That means it must be in A′ and also in B′, which is precisely membership in A′ ∩ B′. Therefore, option B is correct; A′ ∪ B′ would represent the complement of A ∩ B instead.
Frequently asked questions
What is the correct answer to this question?
A′ ∩ B′
Why is this the correct answer?
De Morgan’s law states that the complement of a union equals the intersection of the complements: (A ∪ B)′ = A′ ∩ B′. An element lies outside A ∪ B only when it belongs to neither A nor B. That means it must be in A′ and also in B′, which is precisely membership in A′ ∩ B′. Therefore, option B is correct; A′ ∪ B′ would represent the complement of A ∩ B instead.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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