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Subjects
Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If P(A) has 256 elements, how many elements are in P(P(A))?

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Answer and explanation

Correct answer: 2²⁵⁶

The statement |P(A)| = 256 means that P(A) itself is a set containing 256 elements. The power set of any finite set with n elements contains 2ⁿ elements, since every element has two choices: included or excluded. Therefore |P(P(A))| = 2²⁵⁶, not 256² or 2⁸.

Tags

setspower-setiterated-power-setcardinalityPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2²⁵⁶

Why is this the correct answer?

The statement |P(A)| = 256 means that P(A) itself is a set containing 256 elements. The power set of any finite set with n elements contains 2ⁿ elements, since every element has two choices: included or excluded. Therefore |P(P(A))| = 2²⁵⁶, not 256² or 2⁸.

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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