If U = {1,2,3,4,5,6}, A = {1,2,4}, and B = {2,4,6}, what is Aᶜ ∩ Bᶜ?
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Answer and explanation
Correct answer: {3,5}
Calculate each complement within U: Aᶜ = {3,5,6} and Bᶜ = {1,3,5}. Their common elements are 3 and 5, so Aᶜ ∩ Bᶜ = {3,5}. De Morgan’s law gives the same result because Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ, A ∪ B = {1,2,4,6}, and its complement is {3,5}. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3,5}
Why is this the correct answer?
Calculate each complement within U: Aᶜ = {3,5,6} and Bᶜ = {1,3,5}. Their common elements are 3 and 5, so Aᶜ ∩ Bᶜ = {3,5}. De Morgan’s law gives the same result because Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ, A ∪ B = {1,2,4,6}, and its complement is {3,5}. Therefore 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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