If A = {x,y,z}, how many singleton sets are there in P(P(A))?
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Answer and explanation
Correct answer: 8
Since A has three elements, P(A) has 2^3 = 8 elements. A singleton subset of any set contains exactly one element. Therefore, for each of the eight elements of P(A), there is one singleton subset containing it. These eight singleton subsets belong to P(P(A)), so the required number is 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Since A has three elements, P(A) has 2^3 = 8 elements. A singleton subset of any set contains exactly one element. Therefore, for each of the eight elements of P(A), there is one singleton subset containing it. These eight singleton subsets belong to P(P(A)), so the required number is 8.
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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