If A = ∅, what is P(P(A))?
Answer and explanation
Correct answer: {∅,{∅}}
The power set of the empty set contains exactly one subset, namely the empty set itself: P(∅) = {∅}. Now take the power set of the one-element set {∅}. Its subsets are the empty set and the set containing its only element, namely {∅}. Therefore P(P(A)) = P({∅}) = {∅,{∅}}. Notice that ∅ and {∅} are different: the first has no elements, while the second has one element. Hence option D is correct.
Frequently asked questions
What is the correct answer to this question?
{∅,{∅}}
Why is this the correct answer?
The power set of the empty set contains exactly one subset, namely the empty set itself: P(∅) = {∅}. Now take the power set of the one-element set {∅}. Its subsets are the empty set and the set containing its only element, namely {∅}. Therefore P(P(A)) = P({∅}) = {∅,{∅}}. Notice that ∅ and {∅} are different: the first has no elements, while the second has one element. Hence option D is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
