If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 7}, and B = {2, 3, 8}, what is (A ∪ B)ᶜ?
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Answer and explanation
Correct answer: {4, 5, 6}
First form the union by collecting every element appearing in A or B: A ∪ B = {1, 2, 3, 7, 8}. The complement of this union contains the elements of U that are absent from the union. Removing 1, 2, 3, 7, and 8 from U leaves {4, 5, 6}. Hence (A ∪ B)ᶜ = {4, 5, 6}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{4, 5, 6}
Why is this the correct answer?
First form the union by collecting every element appearing in A or B: A ∪ B = {1, 2, 3, 7, 8}. The complement of this union contains the elements of U that are absent from the union. Removing 1, 2, 3, 7, and 8 from U leaves {4, 5, 6}. Hence (A ∪ B)ᶜ = {4, 5, 6}, 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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