If A = {∅, 1, {1}}, how many members are there in 𝒫(A)?
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Answer and explanation
Correct answer: 8
The elements of A are ∅, the number 1, and the set {1}. These are three distinct objects: 1 is not the same as {1}, and ∅ is different from both. Hence |A| = 3. The power set of a set with n elements has 2^n members, including the empty subset and the complete set. Therefore |𝒫(A)| = 2^3 = 8, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The elements of A are ∅, the number 1, and the set {1}. These are three distinct objects: 1 is not the same as {1}, and ∅ is different from both. Hence |A| = 3. The power set of a set with n elements has 2^n members, including the empty subset and the complete set. Therefore |𝒫(A)| = 2^3 = 8, so option C 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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