Which description correctly represents G = {4, 9, 16, 25} in set-builder form?
Answer and explanation
Correct answer: G = {x : x = n², n ∈ ℕ, 2 ≤ n ≤ 5} — G = {x : x = n², n ∈ ℕ, 2 ≤ n ≤ 5}
The elements 4, 9, 16, and 25 are the squares of 2, 3, 4, and 5 respectively: 4 = 2², 9 = 3², 16 = 4², and 25 = 5². Therefore the rule is x = n² with n restricted to the natural numbers from 2 through 5. Starting at n = 1 would incorrectly include 1, so option B is not correct. Hence option A gives the exact set-builder form.
Frequently asked questions
What is the correct answer to this question?
G = {x : x = n², n ∈ ℕ, 2 ≤ n ≤ 5} — G = {x : x = n², n ∈ ℕ, 2 ≤ n ≤ 5}
Why is this the correct answer?
The elements 4, 9, 16, and 25 are the squares of 2, 3, 4, and 5 respectively: 4 = 2², 9 = 3², 16 = 4², and 25 = 5². Therefore the rule is x = n² with n restricted to the natural numbers from 2 through 5. Starting at n = 1 would incorrectly include 1, so option B is not correct. Hence option A gives the exact set-builder form.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
