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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 10

If A = {∅, {1}}, then what is n(P(A))?

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Answer and explanation

Correct answer: 4

The set A has exactly two elements: the empty set ∅ and the singleton set {1}. The fact that ∅ itself is an element does not change the count. For any finite set with n elements, its power set contains 2ⁿ subsets, because each element can either be selected or not selected. Therefore, n(P(A)) = 2² = 4.

Tags

setspower-setcardinalityempty-setPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

The set A has exactly two elements: the empty set ∅ and the singleton set {1}. The fact that ∅ itself is an element does not change the count. For any finite set with n elements, its power set contains 2ⁿ subsets, because each element can either be selected or not selected. Therefore, n(P(A)) = 2² = 4.

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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