If A = {p, q, r, s}, how many one-element (singleton) subsets are in 𝒫(A)?
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Answer and explanation
Correct answer: 4
A singleton subset contains exactly one element. Since A has four elements, p, q, r, and s, the singleton subsets are {p}, {q}, {r}, and {s}. Thus, 𝒫(A) contains four singleton subsets. In general, an n-element set has exactly n singleton subsets, although its total number of subsets is 2ⁿ; here the total is 2⁴ = 16.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A singleton subset contains exactly one element. Since A has four elements, p, q, r, and s, the singleton subsets are {p}, {q}, {r}, and {s}. Thus, 𝒫(A) contains four singleton subsets. In general, an n-element set has exactly n singleton subsets, although its total number of subsets is 2ⁿ; here the total is 2⁴ = 16.
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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