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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 4

If A = {x : x ∈ ℤ, x² - 1 = 0} and B = {-1, 1}, what is the correct conclusion?

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Answer and explanation

Correct answer: A = B

Solve the defining equation: x² - 1 = 0 can be factored as (x - 1)(x + 1) = 0. Therefore, x = 1 or x = -1. Both values belong to the integers, so A = {-1, 1}. This is exactly the set B. Set elements may be written in either order, so the different possible ordering does not make the sets unequal.

Tags

setsequal setsquadratic equationintegersThe 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?

Solve the defining equation: x² - 1 = 0 can be factored as (x - 1)(x + 1) = 0. Therefore, x = 1 or x = -1. Both values belong to the integers, so A = {-1, 1}. This is exactly the set B. Set elements may be written in either order, so the different possible ordering does not make the sets unequal.

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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