For the set A = {x ∈ ℕ : x divides 0}, which statement is correct?
Answer and explanation
Correct answer: A is infinite
Every positive natural number divides 0 because 0 = x × 0 for every natural number x. Thus 1, 2, 3, 4, and infinitely many other natural numbers satisfy the condition. Therefore A contains infinitely many elements and is an infinite set. This is different from division by zero, which is undefined; here we are asking whether a number divides zero.
Frequently asked questions
What is the correct answer to this question?
A is infinite
Why is this the correct answer?
Every positive natural number divides 0 because 0 = x × 0 for every natural number x. Thus 1, 2, 3, 4, and infinitely many other natural numbers satisfy the condition. Therefore A contains infinitely many elements and is an infinite set. This is different from division by zero, which is undefined; here we are asking whether a number divides zero.
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.
