If A = {x : x ∈ ℤ and x² − 1 = 0} and B = {x : x ∈ ℤ, −2 < x < 2 and x ≠ 0}, which of the following is true?
Answer and explanation
Correct answer: A = B
For set A, solve x² − 1 = 0. Factoring gives (x − 1)(x + 1) = 0, so x = 1 or x = −1; both are integers. Thus A = {−1, 1}. For set B, the integers strictly between −2 and 2 are −1, 0, and 1. The condition x ≠ 0 removes 0, leaving B = {−1, 1}. Since A and B contain exactly the same elements, A = B. Therefore, option A is correct; B, C, and D are false.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For set A, solve x² − 1 = 0. Factoring gives (x − 1)(x + 1) = 0, so x = 1 or x = −1; both are integers. Thus A = {−1, 1}. For set B, the integers strictly between −2 and 2 are −1, 0, and 1. The condition x ≠ 0 removes 0, leaving B = {−1, 1}. Since A and B contain exactly the same elements, A = B. Therefore, option A is correct; B, C, and D are false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
