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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If |U| = 14, A ⊆ U, and |𝒫(A)| = 64, what is the value of |𝒫(A′)|?

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Answer and explanation

Correct answer: 2^8

For any finite set X, |𝒫(X)| = 2^|X|. Since |𝒫(A)| = 64 = 2^6, we obtain |A| = 6. Because A is a subset of U and |U| = 14, its complement has |A′| = 14 − 6 = 8 elements. Therefore the power set of A′ contains 2^8 subsets. Thus option C, 2^8, is correct.

Tags

setscardinalitypower setcomplementuniversal setPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2^8

Why is this the correct answer?

For any finite set X, |𝒫(X)| = 2^|X|. Since |𝒫(A)| = 64 = 2^6, we obtain |A| = 6. Because A is a subset of U and |U| = 14, its complement has |A′| = 14 − 6 = 8 elements. Therefore the power set of A′ contains 2^8 subsets. Thus option C, 2^8, 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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