If U = {1,2,3,4,5,6,7,8}, A = {1,2,3}, and B = {3,4,5}, what is |𝒫((A ∪ B)′)|?
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Answer and explanation
Correct answer: 8
The union combines every element appearing in either set: A ∪ B = {1,2,3,4,5}. Taking the complement relative to U leaves (A ∪ B)′ = {6,7,8}, which has 3 elements. The power set of a three-element set has 2^3 = 8 members, including the empty subset. Therefore |𝒫((A ∪ B)′)| = 8, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The union combines every element appearing in either set: A ∪ B = {1,2,3,4,5}. Taking the complement relative to U leaves (A ∪ B)′ = {6,7,8}, which has 3 elements. The power set of a three-element set has 2^3 = 8 members, including the empty subset. Therefore |𝒫((A ∪ B)′)| = 8, so option C 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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