If A = {∅, {∅}}, which of the following is an element of the power set P(A)?
Answer and explanation
Correct answer: All of these
The set A has exactly two elements: ∅ and {∅}. Its power set therefore contains every subset of A: ∅, {∅}, {{∅}}, and {∅, {∅}}. Option A is the empty subset, option B contains the element ∅, and option C contains the element {∅}. Thus all three are subsets of A and hence all three are elements of P(A). Therefore, the correct answer is D, All of these.
Frequently asked questions
What is the correct answer to this question?
All of these
Why is this the correct answer?
The set A has exactly two elements: ∅ and {∅}. Its power set therefore contains every subset of A: ∅, {∅}, {{∅}}, and {∅, {∅}}. Option A is the empty subset, option B contains the element ∅, and option C contains the element {∅}. Thus all three are subsets of A and hence all three are elements of P(A). Therefore, the correct answer is D, All of these.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
