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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 6

Choose the correct conclusion for the set {x ∈ N : x divides 0}, where N denotes the positive natural numbers.

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Answer and explanation

Correct answer: Infinite set

A positive integer x divides 0 because 0 = x × 0, so the quotient is the integer 0. This is true for every positive natural number: 1, 2, 3, and so on. Since the positive natural numbers are infinite, the set of all such divisors of zero is also infinite. Therefore, option C is correct.

Tags

setsinfinite setsdivisibilitynatural numbersThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

Infinite set

Why is this the correct answer?

A positive integer x divides 0 because 0 = x × 0, so the quotient is the integer 0. This is true for every positive natural number: 1, 2, 3, and so on. Since the positive natural numbers are infinite, the set of all such divisors of zero is also infinite. Therefore, 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.

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