If A = {∅, {∅}, {{∅}}}, what is |𝒫(A)|?
Answer and explanation
Correct answer: 8
The three displayed objects are distinct elements of A: the empty set ∅, the singleton set {∅}, and the singleton set containing {∅}, namely {{∅}}. Although they are nested and visually similar, they are not equal sets. Thus |A| = 3. The power set of an n-element set contains 2^n subsets, so |𝒫(A)| = 2^3 = 8. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The three displayed objects are distinct elements of A: the empty set ∅, the singleton set {∅}, and the singleton set containing {∅}, namely {{∅}}. Although they are nested and visually similar, they are not equal sets. Thus |A| = 3. The power set of an n-element set contains 2^n subsets, so |𝒫(A)| = 2^3 = 8. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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