Question

Which of the following statements is true?
(i) Every natural number is a rational number.
(ii) Every integer is a rational number.
(iii) $0$ is a whole number but it is not a rational number

• A. Both (i) and (ii) are true
• B. All the given statements are true
• C. Only (ii) is true
• D. Only (iii) is true

Answer 1

The correct option is A Both (i) and (ii) are true

Solution: A number which can be expressed in the form of $\frac{p}{q}$ where p and q are integers and
$q\ne 0$ is called a rational number.
Since every natural number can be expressed in the form of a rational number by taking $1$ as the
denominator, such as and $\frac{1}{1}$ and $\frac{2}{1}$, every natural number is a rational number too.

Therefore, statement (i) is true.
Similarly, every integer can be expressed in the form of a rational number by taking the denominator as $1$,
such as $\frac{-2}{1},\frac{-2}{1},\frac{0}{1},\frac{1}{1},\frac{2}{1}$. So, every integer is a rational number too.

Therefore, statement (ii) is true.
$0$, being an integer, is a rational number.
Therefore, statement (iii) is not true.