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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If A = {∅, {∅}}, what is n(P(A))?

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Answer and explanation

Correct answer: 4

The set A has two distinct elements: the empty set ∅ and the singleton set {∅}. Although one is formed from the other, they are not equal; ∅ has no elements, whereas {∅} has one element, namely ∅. Therefore |A| = 2, and the power set has 2² = 4 elements: ∅, {∅}, {{∅}}, and {∅,{∅}}. Option C is correct.

Tags

setsempty setpower setnested setsMathematicsPower Set and SubsetsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

The set A has two distinct elements: the empty set ∅ and the singleton set {∅}. Although one is formed from the other, they are not equal; ∅ has no elements, whereas {∅} has one element, namely ∅. Therefore |A| = 2, and the power set has 2² = 4 elements: ∅, {∅}, {{∅}}, and {∅,{∅}}. 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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