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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 9

If A = {a, b, c, d, e}, how many proper subsets of A do not contain a?

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Answer and explanation

Correct answer: 16

Any subset that does not contain a can use only the remaining four elements b, c, d, and e. Each of these four elements may either be included or excluded, so the number of such subsets is 2^4 = 16. None of them can equal A because A contains a, so every one of these 16 subsets is proper. Therefore option C is correct.

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proper-subsetspower-setcountingsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

16

Why is this the correct answer?

Any subset that does not contain a can use only the remaining four elements b, c, d, and e. Each of these four elements may either be included or excluded, so the number of such subsets is 2^4 = 16. None of them can equal A because A contains a, so every one of these 16 subsets is proper. 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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