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Subjects
Class 10MathematicsSetsPower Set and SubsetsEasyLevel 10

If P(A) = {∅, {5}}, what is the original set A?

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Answer and explanation

Correct answer: {5}

For any set A, its power set P(A) always contains the empty set and A itself. Here P(A) has exactly two elements: ∅ and {5}. Since the non-empty member is the whole original set, A must be {5}. This also agrees with the rule that a one-element set has 2¹ = 2 subsets: ∅ and {5}.

Tags

setspower_setsubsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{5}

Why is this the correct answer?

For any set A, its power set P(A) always contains the empty set and A itself. Here P(A) has exactly two elements: ∅ and {5}. Since the non-empty member is the whole original set, A must be {5}. This also agrees with the rule that a one-element set has 2¹ = 2 subsets: ∅ and {5}.

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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