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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsHardLevel 10

If A = {x ∈ ℤ : x is a multiple of 0}, what is A equal to?

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Answer and explanation

Correct answer: {0}

A multiple of 0 has the form 0 × k, where k is an integer. Regardless of the value of k, 0 × k = 0. Therefore the only integer that can be a multiple of 0 is 0 itself, and A = {0}. It is not ℤ, because nonzero integers cannot be written as 0 times an integer. Hence option B is correct.

Tags

setsmultiples-of-zerosingleton-setThe 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?

{0}

Why is this the correct answer?

A multiple of 0 has the form 0 × k, where k is an integer. Regardless of the value of k, 0 × k = 0. Therefore the only integer that can be a multiple of 0 is 0 itself, and A = {0}. It is not ℤ, because nonzero integers cannot be written as 0 times an integer. Hence option B 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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