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Class 10MathematicsSetsPower Set and SubsetsHardLevel 10

If A={∅,{∅}}, what is |P(A)|?

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Answer and explanation

Correct answer: 4

Although ∅ and {∅} look related, they are different objects: ∅ has no elements, while {∅} has one element, namely ∅. Thus A has two distinct members. For a finite set with n members, the power set has 2^n members. Therefore |P(A)|=2^2=4, so option C is correct.

Tags

setsnested-setscardinalitypower-setPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

Although ∅ and {∅} look related, they are different objects: ∅ has no elements, while {∅} has one element, namely ∅. Thus A has two distinct members. For a finite set with n members, the power set has 2^n members. Therefore |P(A)|=2^2=4, so 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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