Which set is equal to K = {0, 1, 4, 9, 16}?
Answer and explanation
Correct answer: {x : x = n², n ∈ ℤ, 0 ≤ n ≤ 4}
The elements of K are the squares 0², 1², 2², 3², and 4². Therefore, allowing n to be an integer from 0 through 4 produces exactly {0, 1, 4, 9, 16}. Option A also includes n = 5 and therefore includes 25, so it is not equal to K. The other options produce consecutive or even numbers, not precisely the required squares.
Frequently asked questions
What is the correct answer to this question?
{x : x = n², n ∈ ℤ, 0 ≤ n ≤ 4}
Why is this the correct answer?
The elements of K are the squares 0², 1², 2², 3², and 4². Therefore, allowing n to be an integer from 0 through 4 produces exactly {0, 1, 4, 9, 16}. Option A also includes n = 5 and therefore includes 25, so it is not equal to K. The other options produce consecutive or even numbers, not precisely the required squares.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
