If A is a subset of the universal set U, what is (A′)′?
Answer and explanation
Correct answer: A
The double-complement law states that taking the complement twice returns the original set: (A′)′ = A. The first complement contains all elements of U that are not in A. Taking its complement removes those elements and retains exactly the elements originally in A. This result depends on using the same universal set U for both complements. Hence option A is correct, while A′, U, and ∅ are not generally equal to (A′)′.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
The double-complement law states that taking the complement twice returns the original set: (A′)′ = A. The first complement contains all elements of U that are not in A. Taking its complement removes those elements and retains exactly the elements originally in A. This result depends on using the same universal set U for both complements. Hence option A is correct, while A′, U, and ∅ are not generally equal to (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.
