Which option gives the correct set-builder form of D = {1, 8, 27, 64}?
Answer and explanation
Correct answer: D = {n³ : n ∈ ℕ, 1 ≤ n ≤ 4}
The elements 1, 8, 27, and 64 are the cubes of 1, 2, 3, and 4 respectively: 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore, the set can be described as D = {n³ : n ∈ ℕ and 1 ≤ n ≤ 4}. The other options generate squares, powers of 2, or multiples of 4, so they do not produce exactly the given set.
Frequently asked questions
What is the correct answer to this question?
D = {n³ : n ∈ ℕ, 1 ≤ n ≤ 4}
Why is this the correct answer?
The elements 1, 8, 27, and 64 are the cubes of 1, 2, 3, and 4 respectively: 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore, the set can be described as D = {n³ : n ∈ ℕ and 1 ≤ n ≤ 4}. The other options generate squares, powers of 2, or multiples of 4, so they do not produce exactly the given set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
