If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 2, 7, 8}, which set is A′ ∪ A?
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Answer and explanation
Correct answer: {1, 2, 3, 4, 5, 6, 7, 8}
For any set A contained in a universal set U, the complement A′ contains all elements of U outside A. Here, A′ = {3, 4, 5, 6}. Taking the union of A′ and A combines every element in either set: {3, 4, 5, 6} ∪ {1, 2, 7, 8} = U. Therefore, A′ ∪ A = U, which is option A.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4, 5, 6, 7, 8}
Why is this the correct answer?
For any set A contained in a universal set U, the complement A′ contains all elements of U outside A. Here, A′ = {3, 4, 5, 6}. Taking the union of A′ and A combines every element in either set: {3, 4, 5, 6} ∪ {1, 2, 7, 8} = U. Therefore, A′ ∪ A = U, which is option A.
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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