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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

How many elements does 𝒫(𝒫(∅)) have?

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Answer and explanation

Correct answer: 2

First evaluate the inner power set. Since ∅ has no elements, 𝒫(∅) = {∅}, which has one element. Now take the power set of this one-element set. A one-element set has 2¹ = 2 subsets: ∅ and {∅}. Therefore, 𝒫(𝒫(∅)) contains two elements. The two power-set operations must be applied successively from the inside outward.

Tags

setsiterated power setempty setsubsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2

Why is this the correct answer?

First evaluate the inner power set. Since ∅ has no elements, 𝒫(∅) = {∅}, which has one element. Now take the power set of this one-element set. A one-element set has 2¹ = 2 subsets: ∅ and {∅}. Therefore, 𝒫(𝒫(∅)) contains two elements. The two power-set operations must be applied successively from the inside outward.

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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