Which option gives the correct set-builder form for {0, 1, 8, 27, 64}?
Answer and explanation
Correct answer: {x : x = n³, n ∈ W, 0 ≤ n ≤ 4}
The listed numbers are consecutive cubes: 0 = 0³, 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore each element can be written as x = n³, where n is a whole number from 0 through 4. The square, linear, and exponential expressions in the other choices do not generate this complete list. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{x : x = n³, n ∈ W, 0 ≤ n ≤ 4}
Why is this the correct answer?
The listed numbers are consecutive cubes: 0 = 0³, 1 = 1³, 8 = 2³, 27 = 3³, and 64 = 4³. Therefore each element can be written as x = n³, where n is a whole number from 0 through 4. The square, linear, and exponential expressions in the other choices do not generate this complete list. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
