Classify the following statements as true or false. a. 12 is a factor of 168. b. 341 is a multiple of 11. c. \( 13 \mid 403 \) and \( 13 \nmid 29 \) implies \( 13 \nmid(403-29) \). A. Choose the correct answer below. B. The statement is false; 12 does not divide 168 evenly. C. The statement is true; since 12 divides 168 evenly, it is a factor of 168 . 168 is a factor of 12 . D. The statement is true; 168 is a factor of 12 .

Let's evaluate each statement one by one: a. **12 is a factor of 168.** - To determine if 12 is a factor of 168, we can divide 168 by 12. - \( 168 \div 12 = 14 \), which is an integer. - Therefore, 12 is indeed a factor of 168. - This statement is **true**. b. **341 is a multiple of 11.** - To check if 341 is a multiple of 11, we can divide 341 by 11. - \( 341 \div 11 \approx 31 \) with a remainder (since \( 11 \times 31 = 341 \) and \( 341 - 341 = 0 \)). - Therefore, 341 is not a multiple of 11. - This statement is **false**. c. **\( 13 \mid 403 \) and \( 13 \nmid 29 \) implies \( 13 \nmid(403-29) \).** - First, we check if \( 13 \mid 403 \). - \( 403 \div 13 = 31 \), which is an integer, so \( 13 \mid 403 \) is true. - Next, we check if \( 13 \nmid 29 \). - \( 29 \div 13 \approx 2.23 \), which is not an integer, so \( 13 \nmid 29 \) is true. - Now, we calculate \( 403 - 29 = 374 \) and check if \( 13 \mid 374 \). - \( 374 \div 13 \approx 28.77 \), which is not an integer, so \( 13 \nmid 374 \) is true. - Therefore, the implication holds true. - This statement is **true**. Now, let's summarize the answers: - a. True - b. False - c. True For the options provided: - A. Choose the correct answer below. (This is not a statement to classify.) - B. The statement is false; 12 does not divide 168 evenly. (This is incorrect; 12 does divide 168 evenly.) - C. The statement is true; since 12 divides 168 evenly, it is a factor of 168. (This is correct.) - D. The statement is true; 168 is a factor of 12. (This is incorrect; 12 is a factor of 168, not the other way around.) Thus, the correct answer is **C**.