If A = {x,y,z}, how many singleton members are in P(P(A))?
Answer and explanation
Correct answer: 8
The set A has 3 elements, so its power set P(A) has 2³ = 8 elements. In general, for any set S, the singleton members of P(S) are exactly {s} for each s ∈ S. Therefore, P(P(A)) has one singleton member for each member of P(A), giving 8 singleton sets: {∅}, {{x}}, {{y}}, {{z}}, {{x,y}}, {{x,z}}, {{y,z}}, and {{x,y,z}}. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The set A has 3 elements, so its power set P(A) has 2³ = 8 elements. In general, for any set S, the singleton members of P(S) are exactly {s} for each s ∈ S. Therefore, P(P(A)) has one singleton member for each member of P(A), giving 8 singleton sets: {∅}, {{x}}, {{y}}, {{z}}, {{x,y}}, {{x,z}}, {{y,z}}, and {{x,y,z}}. Hence, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
