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

For A = {x ∈ ℝ : x² = x} and B = {0, 1}, which statement is correct?

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Answer and explanation

Correct answer: A = B

Rewrite the equation as x² − x = 0 and factor it: x(x − 1) = 0. By the zero-product property, x = 0 or x = 1. Both are real numbers, so A = {0, 1}. Since B is defined as {0, 1}, A and B have exactly the same elements. Therefore, A = B, and the set is finite with two elements.

Tags

setsequal setssolution setfactorisationThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

Rewrite the equation as x² − x = 0 and factor it: x(x − 1) = 0. By the zero-product property, x = 0 or x = 1. Both are real numbers, so A = {0, 1}. Since B is defined as {0, 1}, A and B have exactly the same elements. Therefore, A = B, and the set is finite with two elements.

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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