Question

Which of the following statements are 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. (i), (ii) and (iii)
• B. (i) and (ii)
• C. (i)
• D. (ii) and (iii)

Answer 1

The correct option is B

(i) and (ii)

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 $(\frac{1}{1}$, $\frac{2}{1})$,
each natural number is a rational number too.
Therefore, (i) is true.

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

0, being an integer, is a rational number.
Hence statement (iii) is incorrect.