If A = {{1}, 2}, what is n(P(A))?
Answer and explanation
Correct answer: 4
The elements of A are the set {1} and the number 2, so A has exactly two elements. The power set P(A) contains every subset of A, including the empty set, two one-element subsets, and A itself. A set with n elements has 2ⁿ subsets; therefore n(P(A)) = 2² = 4. The nested braces do not create an additional element beyond {1}.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The elements of A are the set {1} and the number 2, so A has exactly two elements. The power set P(A) contains every subset of A, including the empty set, two one-element subsets, and A itself. A set with n elements has 2ⁿ subsets; therefore n(P(A)) = 2² = 4. The nested braces do not create an additional element beyond {1}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
