If A has 0 elements, how many elements will 𝒫(A) have?
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Answer and explanation
Correct answer: 1
A set with zero elements is the empty set, written as ∅. For a finite set with n elements, the number of elements in its power set is 2ⁿ. Here n = 0, so |𝒫(A)| = 2⁰ = 1. In fact, 𝒫(∅) = {∅}; the power set has one element, namely the empty set itself. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
A set with zero elements is the empty set, written as ∅. For a finite set with n elements, the number of elements in its power set is 2ⁿ. Here n = 0, so |𝒫(A)| = 2⁰ = 1. In fact, 𝒫(∅) = {∅}; the power set has one element, namely the empty set itself. Therefore, option B is correct.
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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