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

What type of set is {x ∈ ℝ : x² − 2x + 1 = 0}?

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Answer and explanation

Correct answer: Singleton set

Factor the equation: x² − 2x + 1 = (x − 1)². Setting this equal to zero gives (x − 1)² = 0, so x = 1 is the only real solution. Therefore, the set is {1}, which contains exactly one element. A set with exactly one element is called a singleton set. Hence, option B is the correct answer.

Tags

setssingleton setfinite setquadratic equationreal numbersThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematics

Frequently asked questions

What is the correct answer to this question?

Singleton set

Why is this the correct answer?

Factor the equation: x² − 2x + 1 = (x − 1)². Setting this equal to zero gives (x − 1)² = 0, so x = 1 is the only real solution. Therefore, the set is {1}, which contains exactly one element. A set with exactly one element is called a singleton set. Hence, option B is the correct answer.

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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