Let U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4,5}, and B = {4,5,6,7}. What is the cardinality of P(A' ∪ B')?
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Answer and explanation
Correct answer: 128
By De Morgan’s law, A' ∪ B' = (A ∩ B)'. The intersection A ∩ B is {4,5}, containing 2 elements. Its complement in the 9-element universal set U therefore contains 9 - 2 = 7 elements. The power set of a 7-element set has 2^7 = 128 members. Hence option D is correct.
Frequently asked questions
What is the correct answer to this question?
128
Why is this the correct answer?
By De Morgan’s law, A' ∪ B' = (A ∩ B)'. The intersection A ∩ B is {4,5}, containing 2 elements. Its complement in the 9-element universal set U therefore contains 9 - 2 = 7 elements. The power set of a 7-element set has 2^7 = 128 members. Hence option D 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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