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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 5

If A is the set of natural numbers whose square is 25, then A is equal to which set?

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Answer and explanation

Correct answer: {5}

We need natural numbers n such that n² = 25. Over the integers, the equation has two solutions, n = 5 and n = −5. However, the question restricts n to natural numbers, and −5 is not natural. Since 5² = 25, the only allowed element is 5. Therefore, A = {5}, a singleton set.

Tags

setsnatural-numberssquare-equationsingleton-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?

{5}

Why is this the correct answer?

We need natural numbers n such that n² = 25. Over the integers, the equation has two solutions, n = 5 and n = −5. However, the question restricts n to natural numbers, and −5 is not natural. Since 5² = 25, the only allowed element is 5. Therefore, A = {5}, a singleton set.

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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