If A = {∅, 1}, what is n(𝒫(A))?
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Answer and explanation
Correct answer: 4
The set A has two distinct elements: the empty set ∅ and the number 1. The fact that one element is itself a set does not change the count; thus n(A) = 2. A finite set with n elements has 2ⁿ subsets, so n(𝒫(A)) = 2² = 4. Its subsets are ∅, {∅}, {1}, and {∅, 1}.
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 number 1. The fact that one element is itself a set does not change the count; thus n(A) = 2. A finite set with n elements has 2ⁿ subsets, so n(𝒫(A)) = 2² = 4. Its subsets are ∅, {∅}, {1}, and {∅, 1}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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