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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 7

If a set has 31 proper subsets, how many elements does the set have?

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Answer and explanation

Correct answer: 5

If a finite set has n elements, its total number of subsets is 2ⁿ. A proper subset includes every subset except the set itself, so the number of proper subsets is 2ⁿ − 1. Given 2ⁿ − 1 = 31, we obtain 2ⁿ = 32 = 2⁵. Therefore n = 5, making option B correct. The empty set is included among the proper subsets.

Tags

setsproper subsetspower setexponentsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

5

Why is this the correct answer?

If a finite set has n elements, its total number of subsets is 2ⁿ. A proper subset includes every subset except the set itself, so the number of proper subsets is 2ⁿ − 1. Given 2ⁿ − 1 = 31, we obtain 2ⁿ = 32 = 2⁵. Therefore n = 5, making option B correct. The empty set is included among the proper subsets.

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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