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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If A = ∅, how many members are there in P(P(P(A)))?

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Answer and explanation

Correct answer: 4

Start with A = ∅, which has 0 elements. Its power set is P(A) = {∅}, so |P(A)| = 1. Taking the power set again gives a set with 2¹ = 2 elements, so |P(P(A))| = 2. Taking the power set a third time gives 2² = 4 elements. Therefore, |P(P(P(A)))| = 4, making option B correct.

Tags

setsempty-setiterated-power-setcardinalitypower-setPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

Start with A = ∅, which has 0 elements. Its power set is P(A) = {∅}, so |P(A)| = 1. Taking the power set again gives a set with 2¹ = 2 elements, so |P(P(A))| = 2. Taking the power set a third time gives 2² = 4 elements. Therefore, |P(P(P(A)))| = 4, making option B 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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