How many elements are there in the power set 𝒫(∅) of the empty set?
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Answer and explanation
Correct answer: 1
The empty set has zero elements, but it has one subset: itself. The general rule says that a set with n elements has 2ⁿ subsets. Taking n = 0 gives |𝒫(∅)| = 2⁰ = 1. Thus 𝒫(∅) = {∅}, which is a set containing one element. It is important not to confuse the empty set with its power set.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The empty set has zero elements, but it has one subset: itself. The general rule says that a set with n elements has 2ⁿ subsets. Taking n = 0 gives |𝒫(∅)| = 2⁰ = 1. Thus 𝒫(∅) = {∅}, which is a set containing one element. It is important not to confuse the empty set with its power set.
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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