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

If B₁ = {x : x ∈ ℝ, x² = 2}, what type of set is B₁?

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Answer and explanation

Correct answer: Two-element finite set

Solving x² = 2 over the real numbers gives x = √2 and x = −√2. Therefore, B₁ = {−√2, √2}, which contains exactly two distinct elements. A set with a fixed, countable number of elements is finite. Thus B₁ is a two-element finite set, not an empty or infinite set.

Tags

setsfinite setreal 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?

Two-element finite set

Why is this the correct answer?

Solving x² = 2 over the real numbers gives x = √2 and x = −√2. Therefore, B₁ = {−√2, √2}, which contains exactly two distinct elements. A set with a fixed, countable number of elements is finite. Thus B₁ is a two-element finite set, not an empty or infinite 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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