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

Which statement is correct about the set {x : x ∈ Z, x² = 2}?

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Answer and explanation

Correct answer: It is the empty set

The equation x² = 2 has the real solutions √2 and −√2, but neither solution is an integer. Since the domain in the set-builder description is Z, only integer solutions may be included. No integer satisfies the equation, so the set has zero elements and is therefore the empty set, ∅.

Tags

setsempty setintegersquadratic equationsThe 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?

It is the empty set

Why is this the correct answer?

The equation x² = 2 has the real solutions √2 and −√2, but neither solution is an integer. Since the domain in the set-builder description is Z, only integer solutions may be included. No integer satisfies the equation, so the set has zero elements and is therefore the empty 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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