If A = {x ∈ ℤ : x² − 1 = 0} and B = {x ∈ ℕ : x² − 1 = 0}, which statement is correct?
Answer and explanation
Correct answer: A = {−1, 1} and B = {1}
Solving x² − 1 = 0 gives (x − 1)(x + 1) = 0, so x = 1 or x = −1. Both solutions belong to ℤ, hence A = {−1, 1}. Under the usual convention ℕ = {1, 2, 3, ...}, only 1 belongs to the natural numbers, so B = {1}. The domain in a set-builder description determines which solutions are included.
Frequently asked questions
What is the correct answer to this question?
A = {−1, 1} and B = {1}
Why is this the correct answer?
Solving x² − 1 = 0 gives (x − 1)(x + 1) = 0, so x = 1 or x = −1. Both solutions belong to ℤ, hence A = {−1, 1}. Under the usual convention ℕ = {1, 2, 3, ...}, only 1 belongs to the natural numbers, so B = {1}. The domain in a set-builder description determines which solutions are included.
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.
