If A = {x : x is a positive divisor of 18}, what is n(P(A))?
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Answer and explanation
Correct answer: 64
The positive divisors of 18 are 1, 2, 3, 6, 9, and 18, so A has 6 elements. For any finite set with n elements, its power set P(A), the set of all subsets of A, has 2ⁿ elements because each element can either be included or excluded from a subset. Hence n(P(A)) = 2⁶ = 64. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The positive divisors of 18 are 1, 2, 3, 6, 9, and 18, so A has 6 elements. For any finite set with n elements, its power set P(A), the set of all subsets of A, has 2ⁿ elements because each element can either be included or excluded from a subset. Hence n(P(A)) = 2⁶ = 64. Therefore, 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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