How many elements are in the power set of the empty set?
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Answer and explanation
Correct answer: 1
The empty set ∅ has no elements, but it has exactly one subset: the empty set itself. Therefore, its power set is 𝒫(∅) = {∅}, which contains one element. This illustrates the formula n(𝒫(S)) = 2ⁿ, where n is the number of elements in S. For S = ∅, n = 0, so n(𝒫(∅)) = 2⁰ = 1.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The empty set ∅ has no elements, but it has exactly one subset: the empty set itself. Therefore, its power set is 𝒫(∅) = {∅}, which contains one element. This illustrates the formula n(𝒫(S)) = 2ⁿ, where n is the number of elements in S. For S = ∅, n = 0, so n(𝒫(∅)) = 2⁰ = 1.
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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