If A = {x ∈ ℤ : |x| < 2} and B = {−1, 0, 1}, what is the correct conclusion?
Answer and explanation
Correct answer: A = B
The governing concept is equality of sets after interpreting an absolute-value inequality. For integers, |x| < 2 is equivalent to −2 < x < 2. The only integers in this open interval are −1, 0, and 1, so A = {−1, 0, 1}. This is exactly B; therefore A = B and option A is correct. The endpoints −2 and 2 are excluded, but that does not make A empty, and B clearly has only three elements, so it is not infinite.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The governing concept is equality of sets after interpreting an absolute-value inequality. For integers, |x| < 2 is equivalent to −2 < x < 2. The only integers in this open interval are −1, 0, and 1, so A = {−1, 0, 1}. This is exactly B; therefore A = B and option A is correct. The endpoints −2 and 2 are excluded, but that does not make A empty, and B clearly has only three elements, so it is not infinite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
