Which statement is correct for the set H = {x : x ∈ Z, x² ≤ 9}?
Answer and explanation
Correct answer: H = {-3, -2, -1, 0, 1, 2, 3}
For integer x, the inequality x² ≤ 9 is equivalent to |x| ≤ 3, or −3 ≤ x ≤ 3. Every integer in this closed interval satisfies the condition: −3, −2, −1, 0, 1, 2, and 3. Values outside the interval have square greater than 9. Hence option A is the complete roster form; B omits negative integers, C omits the endpoints, and D includes only two values.
Frequently asked questions
What is the correct answer to this question?
H = {-3, -2, -1, 0, 1, 2, 3}
Why is this the correct answer?
For integer x, the inequality x² ≤ 9 is equivalent to |x| ≤ 3, or −3 ≤ x ≤ 3. Every integer in this closed interval satisfies the condition: −3, −2, −1, 0, 1, 2, and 3. Values outside the interval have square greater than 9. Hence option A is the complete roster form; B omits negative integers, C omits the endpoints, and D includes only two values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
