If A = {x ∈ ℝ : x² − 1 < 0}, which statement about A is correct?
Answer and explanation
Correct answer: A is infinite and A = {x ∈ ℝ : −1 < x < 1}
We solve x² − 1 < 0 by adding 1 to both sides, obtaining x² < 1. For real numbers, this is equivalent to −1 < x < 1. Therefore, A is the open interval (−1, 1). Every non-empty real interval contains infinitely many real numbers, so A is an infinite set. The endpoints −1 and 1 are excluded because the inequality is strict.
Frequently asked questions
What is the correct answer to this question?
A is infinite and A = {x ∈ ℝ : −1 < x < 1}
Why is this the correct answer?
We solve x² − 1 < 0 by adding 1 to both sides, obtaining x² < 1. For real numbers, this is equivalent to −1 < x < 1. Therefore, A is the open interval (−1, 1). Every non-empty real interval contains infinitely many real numbers, so A is an infinite set. The endpoints −1 and 1 are excluded because the inequality is strict.
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.
