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

Which set is equal to A = {x ∈ ℤ : x³ = x}?

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Answer and explanation

Correct answer: A = {−1, 0, 1}

We solve the defining equation x³ = x by bringing all terms to one side: x³ − x = 0. Factoring gives x(x² − 1) = 0, and then x(x − 1)(x + 1) = 0. Thus x can be 0, 1, or −1. Each of these is an integer and satisfies the original equation. Since a set lists each element only once, A = {−1, 0, 1}.

Tags

setsfinite setssolution setequal setsThe 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 = {−1, 0, 1}

Why is this the correct answer?

We solve the defining equation x³ = x by bringing all terms to one side: x³ − x = 0. Factoring gives x(x² − 1) = 0, and then x(x − 1)(x + 1) = 0. Thus x can be 0, 1, or −1. Each of these is an integer and satisfies the original equation. Since a set lists each element only once, A = {−1, 0, 1}.

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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