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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If a set B has 1024 total subsets, how many proper subsets does it have?

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Answer and explanation

Correct answer: 1023

If B has n elements, its total number of subsets is 2ⁿ. Since 1024 = 2¹⁰, B has 10 elements. A proper subset is any subset other than the set itself. The total collection P(B) includes B once, so removing that one non-proper subset gives 1024 − 1 = 1023 proper subsets. Therefore, option A is correct.

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setspower setproper subsetscardinalityMathematicsPower Set and SubsetsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

1023

Why is this the correct answer?

If B has n elements, its total number of subsets is 2ⁿ. Since 1024 = 2¹⁰, B has 10 elements. A proper subset is any subset other than the set itself. The total collection P(B) includes B once, so removing that one non-proper subset gives 1024 − 1 = 1023 proper subsets. Therefore, 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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