If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3, 4}, and B = {3, 4, 5}, what is A′ ∩ B′?
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Answer and explanation
Correct answer: {6}
Take each complement relative to U. Since A contains 1, 2, 3, and 4, A′ = {5, 6}. Since B contains 3, 4, and 5, B′ = {1, 2, 6}. The common element in A′ and B′ is therefore only 6. Thus A′ ∩ B′ = {6}, so option A is correct. This also agrees with De Morgan’s law: A′ ∩ B′ = (A ∪ B)′.
Frequently asked questions
What is the correct answer to this question?
{6}
Why is this the correct answer?
Take each complement relative to U. Since A contains 1, 2, 3, and 4, A′ = {5, 6}. Since B contains 3, 4, and 5, B′ = {1, 2, 6}. The common element in A′ and B′ is therefore only 6. Thus A′ ∩ B′ = {6}, so option A is correct. This also agrees with De Morgan’s law: 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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