For any set A, what is (Aᶜ)ᶜ equal to?
Answer and explanation
Correct answer: A, the set A
Taking a complement means selecting all elements of the universal set that are outside the given set. The first complement Aᶜ contains the elements outside A. Taking the complement again selects the elements outside Aᶜ, which are exactly the original elements of A. Therefore, the double-complement law is (Aᶜ)ᶜ = A. Option B is only the first complement, and U or ∅ are not generally equal to the result.
Frequently asked questions
What is the correct answer to this question?
A, the set A
Why is this the correct answer?
Taking a complement means selecting all elements of the universal set that are outside the given set. The first complement Aᶜ contains the elements outside A. Taking the complement again selects the elements outside Aᶜ, which are exactly the original elements of A. Therefore, the double-complement law is (Aᶜ)ᶜ = A. Option B is only the first complement, and U or ∅ are not generally equal to the result.
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.
