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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 4

If D = {x : x ∈ N, x is a factor of 24 and x is a multiple of 4}, which set is D?

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Answer and explanation

Correct answer: D = {4, 8, 12, 24}

The natural factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. We must retain only those factors that are also multiples of 4. These are 4, 8, 12, and 24. The word “and” means both conditions must hold simultaneously, so D = {4, 8, 12, 24}. Therefore option A is correct.

Tags

setsfactorsmultiplesfinite setintersection of conditionsThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematics

Frequently asked questions

What is the correct answer to this question?

D = {4, 8, 12, 24}

Why is this the correct answer?

The natural factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. We must retain only those factors that are also multiples of 4. These are 4, 8, 12, and 24. The word “and” means both conditions must hold simultaneously, so D = {4, 8, 12, 24}. Therefore option A 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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