What is the roster form of Z = {x ∈ Z : x² ≤ 9 and x + 1 > 0}?
Answer and explanation
Correct answer: English: Z = {0, 1, 2, 3} | हिन्दी: Z = {0, 1, 2, 3}
First solve x² ≤ 9. This gives −3 ≤ x ≤ 3, so the possible integers are −3, −2, −1, 0, 1, 2, and 3. Next solve x + 1 > 0, which gives x > −1. Among the possible integers, this retains 0, 1, 2, and 3; −1 is excluded because the inequality is strict. The intersection is therefore Z = {0, 1, 2, 3}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
English: Z = {0, 1, 2, 3} | हिन्दी: Z = {0, 1, 2, 3}
Why is this the correct answer?
First solve x² ≤ 9. This gives −3 ≤ x ≤ 3, so the possible integers are −3, −2, −1, 0, 1, 2, and 3. Next solve x + 1 > 0, which gives x > −1. Among the possible integers, this retains 0, 1, 2, and 3; −1 is excluded because the inequality is strict. The intersection is therefore Z = {0, 1, 2, 3}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
