If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, what is n(P(A' ∩ B'))? Here P denotes the power set.
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Answer and explanation
Correct answer: 4
Using De Morgan’s law, A' ∩ B' = (A ∪ B)'. The union A ∪ B is {1, 2, 3, 4, 5, 6}; therefore its complement in U is {7, 8}. Thus A' ∩ B' has two elements. The power set of any two-element set contains 2² = 4 subsets, including the empty set and the set itself. Therefore the correct answer is option B, 4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Using De Morgan’s law, A' ∩ B' = (A ∪ B)'. The union A ∪ B is {1, 2, 3, 4, 5, 6}; therefore its complement in U is {7, 8}. Thus A' ∩ B' has two elements. The power set of any two-element set contains 2² = 4 subsets, including the empty set and the set itself. Therefore the correct answer is option B, 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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