If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, and B = {4,5,6,7}, what is Aᶜ ∪ Bᶜ?
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Answer and explanation
Correct answer: {1,2,3,6,7,8,9,10}
Apply De Morgan’s law: Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. The common elements of A and B are A ∩ B = {4,5}. The complement of {4,5} relative to U contains every other element of U, namely {1,2,3,6,7,8,9,10}. Hence option A is correct. This also shows why the intersection, not the union, is needed first.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,6,7,8,9,10}
Why is this the correct answer?
Apply De Morgan’s law: Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. The common elements of A and B are A ∩ B = {4,5}. The complement of {4,5} relative to U contains every other element of U, namely {1,2,3,6,7,8,9,10}. Hence option A is correct. This also shows why the intersection, not the union, is needed first.
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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