If A = {x : x ∈ N and 5 < x < 11}, what is n(P(A))?
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Answer and explanation
Correct answer: 32
The natural numbers strictly between 5 and 11 are 6, 7, 8, 9, and 10. Thus A = {6,7,8,9,10} and n(A) = 5. The number of elements in the power set of an n-element set is 2ⁿ. Consequently, n(P(A)) = 2⁵ = 32. Therefore option B is correct; the endpoint values 5 and 11 are not included.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The natural numbers strictly between 5 and 11 are 6, 7, 8, 9, and 10. Thus A = {6,7,8,9,10} and n(A) = 5. The number of elements in the power set of an n-element set is 2ⁿ. Consequently, n(P(A)) = 2⁵ = 32. Therefore option B is correct; the endpoint values 5 and 11 are not included.
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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