For A = {x ∈ ℤ : x² − 1 = 0} and B = {x ∈ ℤ : |x| = 1}, which statement is correct?
Answer and explanation
Correct answer: A = B
The governing idea is equality of sets: two sets are equal when they contain exactly the same elements. For A, x² − 1 = 0 gives x² = 1, so x = 1 or x = −1. For B, |x| = 1 also has the integer solutions x = 1 and x = −1. Therefore A = {−1, 1} and B = {−1, 1}, so A = B. The other choices incorrectly omit a solution or misclassify the set as empty or infinite.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The governing idea is equality of sets: two sets are equal when they contain exactly the same elements. For A, x² − 1 = 0 gives x² = 1, so x = 1 or x = −1. For B, |x| = 1 also has the integer solutions x = 1 and x = −1. Therefore A = {−1, 1} and B = {−1, 1}, so A = B. The other choices incorrectly omit a solution or misclassify the set as empty or infinite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
