If U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4}, B = {3,4,5,6}, and C = {5,6,7,8}, what is (A ∪ B ∪ C)ᶜ?
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Answer and explanation
Correct answer: {9}
First form the union of all three sets. A contributes 1, 2, 3, 4; B adds 5 and 6; and C adds 7 and 8. Thus A ∪ B ∪ C = {1,2,3,4,5,6,7,8}. Since the universal set also contains 9, the only element outside this union is 9. Therefore (A ∪ B ∪ C)ᶜ = {9}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{9}
Why is this the correct answer?
First form the union of all three sets. A contributes 1, 2, 3, 4; B adds 5 and 6; and C adds 7 and 8. Thus A ∪ B ∪ C = {1,2,3,4,5,6,7,8}. Since the universal set also contains 9, the only element outside this union is 9. Therefore (A ∪ B ∪ C)ᶜ = {9}, 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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