Properties of expressions with prime and composite numbers

Since the statements use the permissive modular helper "can be", finding a single valid numerical example validates each statement[cite: 3136, 3139, 3145].

Statement 1: Let p = 5 (prime) and c = 9 (composite). p+c/p-c = 5+9/5-9 = 14/-4, not an integer. Let's try p = 13, c = 9 \rightarrow 13+9/13-9 = 22/4. Let's try p = 7, c = 9 \rightarrow 16/-2 = -8 (even integer). Thus, it can be even. Statement 1 is correct.

Statement 2: 2p + c. Let p = 3 and c = 9. 2(3) + 9 = 6 + 9 = 15 (odd). Thus, it can be odd. Statement 2 is correct.

Statement 3: pc. Let p = 3 and c = 9. 3 × 9 = 27 (odd). Thus, it can be odd. Statement 3 is correct.

All three scenarios are mathematically possible.

Answer: (d).