In the universal set U={1,2,3,4,5,6,7,8}, let A={1,2,3} and B={4,5}. Find Aᶜ∩Bᶜ.
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Answer and explanation
Correct answer: {6,7,8}
With respect to U, Aᶜ={4,5,6,7,8}, because these are the elements not in A. Similarly, Bᶜ={1,2,3,6,7,8}. The common elements of these two complements are 6, 7, and 8. Hence Aᶜ∩Bᶜ={6,7,8}. De Morgan’s law provides the same result: Aᶜ∩Bᶜ=(A∪B)ᶜ, and A∪B={1,2,3,4,5}.
Frequently asked questions
What is the correct answer to this question?
{6,7,8}
Why is this the correct answer?
With respect to U, Aᶜ={4,5,6,7,8}, because these are the elements not in A. Similarly, Bᶜ={1,2,3,6,7,8}. The common elements of these two complements are 6, 7, and 8. Hence Aᶜ∩Bᶜ={6,7,8}. De Morgan’s law provides the same result: Aᶜ∩Bᶜ=(A∪B)ᶜ, and A∪B={1,2,3,4,5}.
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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