Which option is a suitable set-builder form for F₃ = {1, 8, 27, 64}?
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Answer and explanation
Correct answer: {x³ : x ∈ ℕ, 1 ≤ x ≤ 4}
The listed elements are consecutive cubes: 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore, the elements can be described as x³, where x is a natural number from 1 through 4 inclusive. Option A produces squares, option C produces natural numbers, and option D omits 1 and 64. Hence B is correct.
Frequently asked questions
What is the correct answer to this question?
{x³ : x ∈ ℕ, 1 ≤ x ≤ 4}
Why is this the correct answer?
The listed elements are consecutive cubes: 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore, the elements can be described as x³, where x is a natural number from 1 through 4 inclusive. Option A produces squares, option C produces natural numbers, and option D omits 1 and 64. Hence B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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