If A = {x ∈ ℤ : x³ = x}, which of the following is A equal to?
Answer and explanation
Correct answer: {−1, 0, 1}
The governing concept is describing a set by solving its defining equation over the stated domain. From x³ = x, move all terms to one side: x³ − x = 0. Factorisation gives x(x − 1)(x + 1) = 0, so x = 0, 1, or −1. All three values belong to ℤ, and no other roots arise from the factors. Therefore A = {−1, 0, 1}, making option A correct. The other finite options omit one solution, while ℤ includes many values that do not satisfy the equation.
Frequently asked questions
What is the correct answer to this question?
{−1, 0, 1}
Why is this the correct answer?
The governing concept is describing a set by solving its defining equation over the stated domain. From x³ = x, move all terms to one side: x³ − x = 0. Factorisation gives x(x − 1)(x + 1) = 0, so x = 0, 1, or −1. All three values belong to ℤ, and no other roots arise from the factors. Therefore A = {−1, 0, 1}, making option A correct. The other finite options omit one solution, while ℤ includes many values that do not satisfy the 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.
