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

If A = {x : x is a natural number and x² = 2}, what kind of set is A?

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Answer and explanation

Correct answer: Empty set

The equation x² = 2 has real solutions x = √2 and x = −√2, but neither solution is a natural number. In particular, √2 is irrational and is not a member of the natural numbers. Since no natural number satisfies the stated condition, the set contains no elements and is therefore empty.

Tags

setsempty-setnatural-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 set

Why is this the correct answer?

The equation x² = 2 has real solutions x = √2 and x = −√2, but neither solution is a natural number. In particular, √2 is irrational and is not a member of the natural numbers. Since no natural number satisfies the stated condition, the set contains no elements and is therefore empty.

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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