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

Which statement is correct about the set {x : x ∈ ℝ and x² = 0}?

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Answer and explanation

Correct answer: It is {0}, so it is finite

A real number has square zero only when the number itself is zero. Thus the equation x² = 0 has the single solution x = 0, and 0 belongs to ℝ. The set is therefore {0}, which contains exactly one element. A one-element set is called a singleton and is finite, so option A is correct.

Tags

setssingleton-setfinite-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?

It is {0}, so it is finite

Why is this the correct answer?

A real number has square zero only when the number itself is zero. Thus the equation x² = 0 has the single solution x = 0, and 0 belongs to ℝ. The set is therefore {0}, which contains exactly one element. A one-element set is called a singleton and is finite, so 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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