Consider the following in respect of prime number p and composite number c 1. p + c / p - c can be even. 2. 2p + c can be odd. 3. pc can be odd. Which of the statements given above are correct?

Let's analyze each statement: 1. p + c / p - c can be even. For this expression to be even, we need to find a prime p and a composite c such that the result is an even integer. Let p = 3 (an odd prime) and c = 9 (an odd composite number). Then p + c = 3 + 9 = 12 (even) And p - c = 3 - 9 = -6 (even) So, (p + c) / (p - c) = 12 / -6 = -2. Since -2 is an even number, this statement can be true. 2. 2p + c can be odd. The term 2p will always be an even number, regardless of whether p is an even prime (p=2) or an odd prime (p=3, 5, ...). For (Even + c) to be odd, c must be an odd number. Can we find an odd composite number? Yes, for example, c = 9, 15, 21, 25, etc. Let p = 2 (prime) and c = 9 (composite). Then 2p + c = 2(2) + 9 = 4 + 9 = 13. Since 13 is an odd number, this statement can be true. 3. pc can be odd. For the product of two numbers to be odd, both numbers must be odd. So, p must be an odd prime AND c must be an odd composite number. Can we find an odd prime? Yes, p = 3, 5, 7, ... Can we find an odd composite number? Yes, c = 9, 15, 21, 25, ... Let p = 3 (odd prime) and c = 9 (odd composite). Then pc = 3 * 9 = 27. Since 27 is an odd number, this statement can be true. Since all three statements can be true, the correct option is D. The final answer is D