If N₁ = {x : x ∈ ℕ and x = 12/n, n ∈ ℕ}, what is the roster form of N₁?
Answer and explanation
Correct answer: N₁ = {1, 2, 3, 4, 6, 12}
Since x = 12/n must be a natural number and n is natural, n must be a positive divisor of 12. The possible divisors are 1, 2, 3, 4, 6, and 12. Their corresponding x-values are 12, 6, 4, 3, 2, and 1. A set is normally written in increasing order, giving {1, 2, 3, 4, 6, 12}. Option B contains the same members but is not the standard increasing roster form; option C incorrectly includes 5.
Frequently asked questions
What is the correct answer to this question?
N₁ = {1, 2, 3, 4, 6, 12}
Why is this the correct answer?
Since x = 12/n must be a natural number and n is natural, n must be a positive divisor of 12. The possible divisors are 1, 2, 3, 4, 6, and 12. Their corresponding x-values are 12, 6, 4, 3, 2, and 1. A set is normally written in increasing order, giving {1, 2, 3, 4, 6, 12}. Option B contains the same members but is not the standard increasing roster form; option C incorrectly includes 5.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
