Consider the following statements:
I. If \(a\) and \(b\) are composite numbers, then \(a+b\) is always composite.
II. Zero is a natural number but not a whole number.
Which of the above statements is/are correct from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither I nor II
A composite number has a factor other than 1 and itself (4, 6, 8, 9, ...). Natural numbers are 1, 2, 3, ...; whole numbers are 0, 1, 2, 3, ..., that is, the natural numbers together with zero.
I. If \(a\) and \(b\) are composite numbers, then \(a+b\) is always composite. Incorrect. One example is enough to break an “always”: 4 and 9 are composite, but \(4+9=13\) is a prime number.
II. Zero is a natural number but not a whole number. Incorrect. It is the other way round: zero is a whole number but not a natural number, since the natural numbers begin at 1.