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?

To determine why all three statements are correct, we test each with simple examples of prime numbers (p) and composite numbers (c).

Statement 1: p + c divided by p - c can be even. If we choose p = 13 and c = 9, then p + c is 22 and p - c is 4. This does not result in an integer. However, if we choose p = 17 and c = 15, then p + c is 32 and p - c is 2. Dividing 32 by 2 gives 16, which is an even number. Thus, statement 1 is correct.

Statement 2: 2p + c can be odd. The term 2p is always even because any number multiplied by 2 is even. For the sum to be odd, c must be an odd composite number. If we choose p = 3 and c = 9, then 2(3) + 9 equals 15, which is odd. Thus, statement 2 is correct.

Statement 3: pc can be odd. The product of two numbers is odd only if both numbers are odd. If we choose an odd prime like p = 5 and an odd composite like c = 9, their product is 45, which is odd. Thus, statement 3 is correct.

Since all three statements can be true under specific conditions, the correct answer is D (1, 2, and 3).