Consider the following statements : 1. If x and y are composite numbers, then x + y is always composite. 2. There does not exist a natural number which is neither prime nor composite. Which of the above statements is/are correct ?

Answer: Option D

Statement 1. Let x = 4 and y = 15. Then, each one of x and y is a composite number.
But, x + y = 19, which is not composite.
∴ Statement 1 is not true.

Statement 2. We know that 1 is neither prime nor composite.
∴ Statement 2 is not true.
Thus, neither 1 nor 2 is correct.