If A = {∅, {∅}}, what is n(P(A))?
Advertisement
Answer and explanation
Correct answer: 4
The set A has two distinct elements: the empty set ∅ and the singleton set {∅}. Although one element contains the other, they are different sets, so n(A) = 2. A set with n elements has exactly 2^n subsets in its power set. Hence n(P(A)) = 2^2 = 4. The four subsets are ∅, {∅}, {{∅}}, and {∅,{∅}}.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The set A has two distinct elements: the empty set ∅ and the singleton set {∅}. Although one element contains the other, they are different sets, so n(A) = 2. A set with n elements has exactly 2^n subsets in its power set. Hence n(P(A)) = 2^2 = 4. The four subsets are ∅, {∅}, {{∅}}, and {∅,{∅}}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement