If A = {x : x ∈ Z and x² = 1} and B = {-1, 1}, which statement is true?
Answer and explanation
Correct answer: A = B
To determine A, solve x² = 1 over the integers. Factoring gives (x − 1)(x + 1) = 0, so x = 1 or x = −1. Therefore, A = {-1, 1}. Since B has exactly the same elements, A and B are equal sets, and A = B is the only correct statement. Remember that equal sets contain precisely the same elements, regardless of their order.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
To determine A, solve x² = 1 over the integers. Factoring gives (x − 1)(x + 1) = 0, so x = 1 or x = −1. Therefore, A = {-1, 1}. Since B has exactly the same elements, A and B are equal sets, and A = B is the only correct statement. Remember that equal sets contain precisely the same elements, regardless of their order.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
