If J₁ = {x : x ∈ ℕ and x has exactly one positive divisor}, what is J₁?
Answer and explanation
Correct answer: J₁ = {1}
The number 1 has exactly one positive divisor: 1 itself. Every natural number greater than 1 has at least two positive divisors, namely 1 and the number itself, so none of them qualifies. Under the convention in the question, natural numbers start at 1; zero is not considered because divisibility by zero is not defined in the usual positive-divisor sense. Hence J₁ is the singleton set {1}.
Frequently asked questions
What is the correct answer to this question?
J₁ = {1}
Why is this the correct answer?
The number 1 has exactly one positive divisor: 1 itself. Every natural number greater than 1 has at least two positive divisors, namely 1 and the number itself, so none of them qualifies. Under the convention in the question, natural numbers start at 1; zero is not considered because divisibility by zero is not defined in the usual positive-divisor sense. Hence J₁ is the singleton set {1}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
