If U = {1,2,3,4,5,6,7,8}, A′ = {1,4,7}, and B′ = {2,4,8}, what is A ∩ B?
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Answer and explanation
Correct answer: {3,5,6}
By De Morgan’s law, A ∩ B = (A′ ∪ B′)′. The union of the given complements is A′ ∪ B′ = {1,2,4,7,8}. Taking its complement in U leaves the elements of U not in this union: {3,5,6}. Therefore A ∩ B = {3,5,6}. Option D is only A, not the required intersection.
Frequently asked questions
What is the correct answer to this question?
{3,5,6}
Why is this the correct answer?
By De Morgan’s law, A ∩ B = (A′ ∪ B′)′. The union of the given complements is A′ ∪ B′ = {1,2,4,7,8}. Taking its complement in U leaves the elements of U not in this union: {3,5,6}. Therefore A ∩ B = {3,5,6}. Option D is only A, not the required intersection.
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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