If A ⊆ U, what is A ∩ U′ equal to?
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Answer and explanation
Correct answer: ∅
The complement U′ consists of all elements in the universal framework that are not in U. Because U already contains every element under consideration, its complement is the empty set: U′ = ∅. Therefore, A ∩ U′ = A ∩ ∅ = ∅, since the intersection of any set with the empty set is empty. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The complement U′ consists of all elements in the universal framework that are not in U. Because U already contains every element under consideration, its complement is the empty set: U′ = ∅. Therefore, A ∩ U′ = A ∩ ∅ = ∅, since the intersection of any set with the empty set is empty. Thus option A is correct.
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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