If |A| = 4, how many singleton members are there in P(P(A))?
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Answer and explanation
Correct answer: 16
If a set A has 4 elements, then its power set P(A) has 2^4 = 16 elements. A singleton member of P(P(A)) is a one-element subset whose only element is one member of P(A). There is exactly one singleton subset for each element of P(A), so P(P(A)) contains 16 singleton members. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
If a set A has 4 elements, then its power set P(A) has 2^4 = 16 elements. A singleton member of P(P(A)) is a one-element subset whose only element is one member of P(A). There is exactly one singleton subset for each element of P(A), so P(P(A)) contains 16 singleton members. 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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