Roster form with inequalities

Correct answer: A. B = {8, 9, 10, 11}

Explanation: The governing concept is converting set-builder notation into roster form by listing every value that satisfies the stated condition. Both inequalities use the symbol ≤, so the endpoints 8 and 11 are included. The natural numbers from 8 through 11 are 8, 9, 10, and 11; hence B = {8, 9, 10, 11}, making option A correct. Option C excludes the upper endpoint 11, while option D excludes the lower endpoint 8. Option B excludes both endpoints and therefore contains only the interior values. The order of elements in a set does not matter, but increasing order makes the complete list easy to verify.

Correct answer: A. I = {13, 14, 15}

Explanation: The governing concept is converting strict inequalities into a roster of qualifying natural numbers. The condition 12 < x means x must be greater than 12, while x < 16 means it must be less than 16. Because both signs are strict, neither endpoint 12 nor endpoint 16 is included. The natural numbers strictly between them are 13, 14, and 15. Therefore I = {13, 14, 15}, making option A correct. Option B includes both forbidden endpoints, option C includes 12, and option D includes 16. The answer demonstrates the difference between strict signs (<) and inclusive signs (≤), which is essential when forming a finite roster.