Which set-builder form correctly represents C₁ = {1, 8, 27, 64}?
Answer and explanation
Correct answer: C₁ = {x : x = n³, n ∈ ℕ, 1 ≤ n ≤ 4}
The elements can be written as 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore every element has the form n³, where n is a natural number from 1 through 4. Option A gives squares, option C gives powers of 2, and option D gives an arithmetic sequence, so none of those represents the given set.
Frequently asked questions
What is the correct answer to this question?
C₁ = {x : x = n³, n ∈ ℕ, 1 ≤ n ≤ 4}
Why is this the correct answer?
The elements can be written as 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore every element has the form n³, where n is a natural number from 1 through 4. Option A gives squares, option C gives powers of 2, and option D gives an arithmetic sequence, so none of those represents 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.
