If A = {x ∈ ℕ : x is a factor of 0}, which statement is correct?
Answer and explanation
Correct answer: A = ℕ, so A is infinite
Under the standard school convention that ℕ = {1, 2, 3, …}, every natural number n is a factor of 0 because 0 = n × 0. Hence every element of ℕ belongs to A, so A = ℕ. Since the natural numbers are infinite, A is infinite. This distinguishes factors of zero from multiples of zero, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
A = ℕ, so A is infinite
Why is this the correct answer?
Under the standard school convention that ℕ = {1, 2, 3, …}, every natural number n is a factor of 0 because 0 = n × 0. Hence every element of ℕ belongs to A, so A = ℕ. Since the natural numbers are infinite, A is infinite. This distinguishes factors of zero from multiples of zero, so option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
