If U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5}, and B = {2, 3, 6}, what is A′ ∪ B′?
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Answer and explanation
Correct answer: {1, 2, 4, 5, 6, 7}
Relative to U, A′ = {2, 4, 6, 7}, because these elements are not in A. Similarly, B′ = {1, 4, 5, 7}. Taking their union gives {1, 2, 4, 5, 6, 7}. Therefore A′ ∪ B′ = {1, 2, 4, 5, 6, 7}, so option A is correct. De Morgan’s law provides the same result: A′ ∪ B′ = (A ∩ B)′.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 4, 5, 6, 7}
Why is this the correct answer?
Relative to U, A′ = {2, 4, 6, 7}, because these elements are not in A. Similarly, B′ = {1, 4, 5, 7}. Taking their union gives {1, 2, 4, 5, 6, 7}. Therefore A′ ∪ B′ = {1, 2, 4, 5, 6, 7}, so option A is correct. De Morgan’s law provides the same result: A′ ∪ B′ = (A ∩ B)′.
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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