Which of the following statements are true and which are false?

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.

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