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

What is the type of the set {x ∈ ℤ : x² = 2}?

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Answer and explanation

Correct answer: Empty set

Solving x² = 2 over the real numbers gives x = √2 and x = −√2. Neither value is an integer, because √2 is irrational. Since the domain in the set-builder notation is ℤ, neither real solution is allowed. Thus no integer satisfies the condition, so the set is empty and option A is correct.

Tags

setsempty setintegersirrational 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?

Solving x² = 2 over the real numbers gives x = √2 and x = −√2. Neither value is an integer, because √2 is irrational. Since the domain in the set-builder notation is ℤ, neither real solution is allowed. Thus no integer satisfies the condition, so the set is empty and 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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