Question:
Which of the following statements are true and which are false?
(i) Every whole 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.
Solution:
1. True
A whole number can be expressed as $\frac{a}{b}$, with $b=1$ and $a \geq 0 .$ Thus, every whole number is rational.
2. True
Every integer is a rational number because any integer can be expressed as $\frac{a}{b}$, with $b=1$ and $0>a \geq 0$. Thus, every integer is a rational number.
3. False
$0=\frac{a}{b}$, for $a=0$ and $b \neq 0 .$ Thus, 0 is a rational and whole number.