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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If A = {1, 2, 3, 4}, how many subsets in P(A) have at least three elements?

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Answer and explanation

Correct answer: 5

At least three elements means that a subset may contain exactly three elements or exactly four elements. The number of three-element subsets is C(4,3) = 4, and the number of four-element subsets is C(4,4) = 1. Adding them gives 4 + 1 = 5. Hence option B is correct; counting only three-element subsets would miss A itself.

Tags

setspower setcombinationssubsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

5

Why is this the correct answer?

At least three elements means that a subset may contain exactly three elements or exactly four elements. The number of three-element subsets is C(4,3) = 4, and the number of four-element subsets is C(4,4) = 1. Adding them gives 4 + 1 = 5. Hence option B is correct; counting only three-element subsets would miss A itself.

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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