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

If H = {x : x ∈ N, x is a factor of 25 and x is even}, what type of set is H?

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Answer and explanation

Correct answer: Empty

The natural-number factors of 25 are 1, 5, and 25. All three factors are odd, so none satisfies the additional condition that x must be even. Therefore, H has no elements and H = ∅. A set with no elements is called the empty set. The two conditions must be applied simultaneously, not separately.

Tags

setsempty setfactorseven 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?

Empty

Why is this the correct answer?

The natural-number factors of 25 are 1, 5, and 25. All three factors are odd, so none satisfies the additional condition that x must be even. Therefore, H has no elements and H = ∅. A set with no elements is called the empty set. The two conditions must be applied simultaneously, not separately.

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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