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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If A = {∅}, how many elements does P(A) have?

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Answer and explanation

Correct answer: 2

Although A contains the empty set, A itself is not empty. The set A = {∅} has exactly one element: the empty set. A set with one element has 2^1 = 2 subsets. They are ∅ and {∅}. Therefore, P(A) = {∅, {∅}} and contains two elements. Confusing ∅ with {∅} would incorrectly lead to one, so option B is correct.

Tags

setspower setempty setsubsetsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

2

Why is this the correct answer?

Although A contains the empty set, A itself is not empty. The set A = {∅} has exactly one element: the empty set. A set with one element has 2^1 = 2 subsets. They are ∅ and {∅}. Therefore, P(A) = {∅, {∅}} and contains two elements. Confusing ∅ with {∅} would incorrectly lead to one, so 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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