If T = {x : x ∈ ℕ, x = 12/n, where n ∈ ℕ}, what is T?
Answer and explanation
Correct answer: T = {1, 2, 3, 4, 6, 12}
For x = 12/n to be a natural number, n must be a positive divisor of 12. The positive divisors of 12 are 1, 2, 3, 4, 6, and 12. Substitution gives x-values 12, 6, 4, 3, 2, and 1. Since sets do not depend on order, these values form T = {1, 2, 3, 4, 6, 12}. Zero is not obtained, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
T = {1, 2, 3, 4, 6, 12}
Why is this the correct answer?
For x = 12/n to be a natural number, n must be a positive divisor of 12. The positive divisors of 12 are 1, 2, 3, 4, 6, and 12. Substitution gives x-values 12, 6, 4, 3, 2, and 1. Since sets do not depend on order, these values form T = {1, 2, 3, 4, 6, 12}. Zero is not obtained, so 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.
