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

If A₁ = {x : x ∈ ℤ and x² = 2}, what is A₁?

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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. The condition x ∈ ℤ restricts us to integers only, so no value satisfies both requirements. Therefore A₁ contains no elements and is the empty set, A₁ = ∅.

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. The condition x ∈ ℤ restricts us to integers only, so no value satisfies both requirements. Therefore A₁ contains no elements and is the empty set, A₁ = ∅.

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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