If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}, what is |P((A ∩ B)')|, where the complement is taken relative to U?
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Answer and explanation
Correct answer: 32
First find the intersection: A ∩ B = {3}, so it contains one element. Taking the complement relative to U gives (A ∩ B)' = U − {3} = {1, 2, 4, 5, 6}, which has 5 elements. A set with n elements has 2^n subsets, including the empty set and the set itself. Therefore, |P((A ∩ B)')| = 2^5 = 32, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
First find the intersection: A ∩ B = {3}, so it contains one element. Taking the complement relative to U gives (A ∩ B)' = U − {3} = {1, 2, 4, 5, 6}, which has 5 elements. A set with n elements has 2^n subsets, including the empty set and the set itself. Therefore, |P((A ∩ B)')| = 2^5 = 32, so option B is correct.
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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