Which is the most accurate set-builder form of L = {1, 4, 9, 16, 25}?
Answer and explanation
Correct answer: L = {x : x = n², n ∈ ℕ, 1 ≤ n ≤ 5}
The elements of L are consecutive perfect squares: 1 = 1², 4 = 2², 9 = 3², 16 = 4², and 25 = 5². Thus, allowing n to take the natural-number values from 1 through 5 gives L = {x : x = n², n ∈ ℕ, 1 ≤ n ≤ 5}. The other options produce even numbers, cubes, or many unwanted natural numbers.
Frequently asked questions
What is the correct answer to this question?
L = {x : x = n², n ∈ ℕ, 1 ≤ n ≤ 5}
Why is this the correct answer?
The elements of L are consecutive perfect squares: 1 = 1², 4 = 2², 9 = 3², 16 = 4², and 25 = 5². Thus, allowing n to take the natural-number values from 1 through 5 gives L = {x : x = n², n ∈ ℕ, 1 ≤ n ≤ 5}. The other options produce even numbers, cubes, or many unwanted natural numbers.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
