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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If A has 3 elements, how many non-empty proper subsets of A are there?

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Answer and explanation

Correct answer: 6

A set with n elements has 2^n subsets. When n = 3, A has 2^3 = 8 subsets in total. A proper subset cannot be the set A itself, and a non-empty subset cannot be ∅. Removing these two subsets from the total gives 8 − 2 = 6 non-empty proper subsets. Therefore option B is correct.

Tags

setsproper subsetspower setcountingPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

6

Why is this the correct answer?

A set with n elements has 2^n subsets. When n = 3, A has 2^3 = 8 subsets in total. A proper subset cannot be the set A itself, and a non-empty subset cannot be ∅. Removing these two subsets from the total gives 8 − 2 = 6 non-empty proper subsets. Therefore option B 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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