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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If U = {1,2,...,16}, A is the set of divisors of 16, and B = A', what is n(P(B))?

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Answer and explanation

Correct answer: 2048

The positive divisors of 16 that lie in U are {1,2,4,8,16}, so A has 5 elements. Since U has 16 elements, B = A' has 16 - 5 = 11 elements. The power set of an 11-element set contains 2^11 subsets, which equals 2048. Thus n(P(B)) = 2048 and option A is correct.

Tags

setspower-setdivisorscomplementPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2048

Why is this the correct answer?

The positive divisors of 16 that lie in U are {1,2,4,8,16}, so A has 5 elements. Since U has 16 elements, B = A' has 16 - 5 = 11 elements. The power set of an 11-element set contains 2^11 subsets, which equals 2048. Thus n(P(B)) = 2048 and option A 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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