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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If U = {a, b, c, d}, how many elements of P(U) have a singleton complement?

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Answer and explanation

Correct answer: 4

Let S be a subset of U. If its complement U − S is a singleton, then exactly one element of U is outside S, so S must contain exactly three elements. The number of three-element subsets of a four-element set is C(4,3) = 4. Therefore, exactly four elements of P(U) have singleton complements.

Tags

setspower setcomplementcombinationsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

Let S be a subset of U. If its complement U − S is a singleton, then exactly one element of U is outside S, so S must contain exactly three elements. The number of three-element subsets of a four-element set is C(4,3) = 4. Therefore, exactly four elements of P(U) have singleton complements.

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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