Which option is the roster form of T = {x : x is a natural number and 3 ≤ x ≤ 7}?
Answer and explanation
Correct answer: T = {3, 4, 5, 6, 7}
The governing concept is translating an inclusive bounded condition into roster form. The inequality 3 ≤ x ≤ 7 says that x must be at least 3 and at most 7. Because both inequalities include equality, the endpoints 3 and 7 must be included. The natural numbers satisfying the condition are therefore 3, 4, 5, 6, and 7. Hence T = {3, 4, 5, 6, 7}, making option A correct. Option B leaves out both endpoints, option C omits the upper endpoint 7, and option D omits the lower endpoint 3. No other natural number can satisfy the stated interval. The inclusion signs are the key detail: replacing either ≤ by < would change the corresponding endpoint.
Frequently asked questions
What is the correct answer to this question?
T = {3, 4, 5, 6, 7}
Why is this the correct answer?
The governing concept is translating an inclusive bounded condition into roster form. The inequality 3 ≤ x ≤ 7 says that x must be at least 3 and at most 7. Because both inequalities include equality, the endpoints 3 and 7 must be included. The natural numbers satisfying the condition are therefore 3, 4, 5, 6, and 7. Hence T = {3, 4, 5, 6, 7}, making option A correct. Option B leaves out both endpoints, option C omits the upper endpoint 7, and option D omits the lower endpoint 3. No other natural number can satisfy the stated interval. The inclusion signs are the key detail: replacing either ≤ by < would change the corresponding endpoint.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Common Questions. Topic: General chapter practice.
