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 ?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Answer: Option D

Solution(By Examveda Team)

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.