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
A prime number has only two factors, 1 and itself; a composite number has more than two. The number 1 has only one factor, so it fits neither group.
I. If \(x\) and \(y\) are composite numbers, then \(x+y\) is always composite. Incorrect. One example is enough to break “always”: 4 and 9 are composite, but \(4+9=13\) is a prime.
II. There does not exist a natural number which is neither prime nor composite. Incorrect. Such a number exists: 1 is neither prime nor composite, since it has only one factor.