In the universal set U={1,2,3,4,5,6,7,8,9}, let A={2,4,6,8} and B={1,2,3,4}. If all complements are taken with respect to U, what is (Aᶜ∪B)ᶜ?
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Answer and explanation
Correct answer: {6,8}
The complement of A with respect to U is Aᶜ={1,3,5,7,9}. Therefore, Aᶜ∪B={1,2,3,4,5,7,9}. The elements of U not in this union are 6 and 8, so (Aᶜ∪B)ᶜ={6,8}. The same result follows directly from De Morgan’s law: (Aᶜ∪B)ᶜ=A∩Bᶜ. Since Bᶜ={5,6,7,8,9}, the intersection with A is {6,8}.
Frequently asked questions
What is the correct answer to this question?
{6,8}
Why is this the correct answer?
The complement of A with respect to U is Aᶜ={1,3,5,7,9}. Therefore, Aᶜ∪B={1,2,3,4,5,7,9}. The elements of U not in this union are 6 and 8, so (Aᶜ∪B)ᶜ={6,8}. The same result follows directly from De Morgan’s law: (Aᶜ∪B)ᶜ=A∩Bᶜ. Since Bᶜ={5,6,7,8,9}, the intersection with A is {6,8}.
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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