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Subjects
Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 3

If A = {x ∈ ℝ : x² = 9} and B = {-3, 3}, choose the correct statement about A.

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Answer and explanation

Correct answer: A = B

To determine A, solve x² = 9 over the real numbers. Taking square roots gives x = 3 or x = -3, because both 3² and (-3)² equal 9. Therefore A = {-3, 3}. This is exactly the same collection of elements as B, so A = B. The negative root must not be omitted when solving a square equation.

Tags

setsequal setssolution setquadratic equationsThe 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?

To determine A, solve x² = 9 over the real numbers. Taking square roots gives x = 3 or x = -3, because both 3² and (-3)² equal 9. Therefore A = {-3, 3}. This is exactly the same collection of elements as B, so A = B. The negative root must not be omitted when solving a square equation.

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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