Consider the following statements:
I. If x and y are composite numbers, then x+y is always composite.
II. There does not exist a natural number which is neither prime nor composite.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither I nor II
Statement I fails on a single example: 4 and 9 are both composite, yet 4 + 9 = 13, which is prime. So the sum of two composite numbers need not be composite.
Statement II also fails, because 1 is a natural number that is neither prime nor composite — it has only one factor. Such a number does exist, so neither statement is correct.