Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4, 5, 6}. What is (Aᶜ)ᶜ ∩ {3, 6, 9}?
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Answer and explanation
Correct answer: {3, 6}
The double-complement law states that taking the complement twice returns the original set, so (Aᶜ)ᶜ = A. The required expression therefore becomes A ∩ {3, 6, 9}. Since A = {1, 2, 3, 4, 5, 6}, the common elements are 3 and 6; 9 is not in A. Thus the intersection is {3, 6}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3, 6}
Why is this the correct answer?
The double-complement law states that taking the complement twice returns the original set, so (Aᶜ)ᶜ = A. The required expression therefore becomes A ∩ {3, 6, 9}. Since A = {1, 2, 3, 4, 5, 6}, the common elements are 3 and 6; 9 is not in A. Thus the intersection is {3, 6}, so 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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