If A = {2, 3}, what is the relation of ∅ with 𝒫(A)?
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Answer and explanation
Correct answer: ∅ ∈ 𝒫(A)
The power set 𝒫(A) is the set of all subsets of A. The empty set is a subset of every set, including A, because it has no element that could violate the subset condition. For A = {2, 3}, 𝒫(A) = {∅, {2}, {3}, {2, 3}}. Hence ∅ is an element of 𝒫(A), and option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅ ∈ 𝒫(A)
Why is this the correct answer?
The power set 𝒫(A) is the set of all subsets of A. The empty set is a subset of every set, including A, because it has no element that could violate the subset condition. For A = {2, 3}, 𝒫(A) = {∅, {2}, {3}, {2, 3}}. Hence ∅ is an element of 𝒫(A), and option A 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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