If A = {x ∈ ℤ : x³ = x} and B = {-1, 0, 1}, choose the correct conclusion.
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Answer and explanation
Correct answer: A = B
To determine A, solve x³ = x. Rearranging gives x³ − x = 0, so x(x² − 1) = 0 and therefore x(x − 1)(x + 1) = 0. Hence x = 0, 1, or −1. All these values are integers, so A = {-1, 0, 1}. Since B contains exactly the same elements, A and B are equal sets. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
To determine A, solve x³ = x. Rearranging gives x³ − x = 0, so x(x² − 1) = 0 and therefore x(x − 1)(x + 1) = 0. Hence x = 0, 1, or −1. All these values are integers, so A = {-1, 0, 1}. Since B contains exactly the same elements, A and B are equal sets. Therefore, option A is correct.
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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