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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 9

Let U = {x ∈ N : 1 ≤ x ≤ 15} and A = {x ∈ U : x is divisible by 3}. What is |P(A')|?

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Answer and explanation

Correct answer: 2^10

The universal set U contains the integers 1 through 15, so it has 15 elements. The numbers divisible by 3 are 3, 6, 9, 12, and 15; hence |A| = 5. Its complement A' therefore contains 15 − 5 = 10 elements. A set with 10 elements has 2^10 subsets, so |P(A')| = 2^10. Therefore option C is correct.

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setscomplementpower-setset-builder-notationPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2^10

Why is this the correct answer?

The universal set U contains the integers 1 through 15, so it has 15 elements. The numbers divisible by 3 are 3, 6, 9, 12, and 15; hence |A| = 5. Its complement A' therefore contains 15 − 5 = 10 elements. A set with 10 elements has 2^10 subsets, so |P(A')| = 2^10. Therefore option C 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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