Which statement is correct about the power set of the empty set?
Answer and explanation
Correct answer: 𝒫(∅) = {∅}
The power set of a set is the set containing all its subsets. The empty set has exactly one subset: the empty set itself. Therefore, 𝒫(∅) = {∅}. Notice the distinction between ∅, which has no elements, and {∅}, which has one element—the empty set. This distinction is essential when determining power sets and their cardinalities.
Frequently asked questions
What is the correct answer to this question?
𝒫(∅) = {∅}
Why is this the correct answer?
The power set of a set is the set containing all its subsets. The empty set has exactly one subset: the empty set itself. Therefore, 𝒫(∅) = {∅}. Notice the distinction between ∅, which has no elements, and {∅}, which has one element—the empty set. This distinction is essential when determining power sets and their cardinalities.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
