If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 2, 3, 4, 5}, what is the value of (Aᶜ)ᶜ ∩ {2, 4, 6, 8}?
Answer and explanation
Correct answer: {2, 4}
First, Aᶜ relative to U is {6, 7, 8}. The double-complement law states that taking the complement twice returns the original set, so (Aᶜ)ᶜ = A = {1, 2, 3, 4, 5}. Now intersect this set with {2, 4, 6, 8}. The common elements are only 2 and 4, because 6 and 8 are not in A. Therefore, the required set is {2, 4}, which is option A.
Frequently asked questions
What is the correct answer to this question?
{2, 4}
Why is this the correct answer?
First, Aᶜ relative to U is {6, 7, 8}. The double-complement law states that taking the complement twice returns the original set, so (Aᶜ)ᶜ = A = {1, 2, 3, 4, 5}. Now intersect this set with {2, 4, 6, 8}. The common elements are only 2 and 4, because 6 and 8 are not in A. Therefore, the required set is {2, 4}, 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.
