If L₁ = {x : x ∈ ℤ and −5 < x ≤ 1}, which is the roster form of L₁?
Answer and explanation
Correct answer: L₁ = {-4, -3, -2, -1, 0, 1}
The condition −5 < x excludes −5 because the left inequality is strict. The condition x ≤ 1 includes 1 because the right inequality is inclusive. Therefore, the integers beginning at −4 and ending at 1 are −4, −3, −2, −1, 0, and 1. This complete list is option A; neither endpoint should be handled in the same way.
Frequently asked questions
What is the correct answer to this question?
L₁ = {-4, -3, -2, -1, 0, 1}
Why is this the correct answer?
The condition −5 < x excludes −5 because the left inequality is strict. The condition x ≤ 1 includes 1 because the right inequality is inclusive. Therefore, the integers beginning at −4 and ending at 1 are −4, −3, −2, −1, 0, and 1. This complete list is option A; neither endpoint should be handled in the same way.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
