 # State whether the following statements are true or false. Give reasons for your answer.

Question:

State whether the following statements are true or false. Give reasons for your answer.
(i) Every natural number is a whole number.
(ii) Every whole number is a natural number.
(iii) Every integer is a whole number.
(iv) Every integer is a rational number.
(v) Every rational number is an integer.
(vi) Every rational number is a whole number.

Solution:

(i) Every natural number is a whole number.
True, since natural numbers are counting numbers i.e N = 1, 2,...
Whole numbers are natural numbers together with 0. i.e W = 0, 1, 2,...
So, every natural number is a whole number

(ii) Every whole number is a natural number.
False, as whole numbers contain natural numbers and 0 whereas natural numbers only contain the counting numbers except 0.

(iii) Every integer is a whole number.
False, whole numbers are natural numbers together with a zero whereas integers include negative numbers also.

(iv) Every integer is a rational number.

True, as rational numbers are of the form $\frac{p}{q}$ where $q \neq 0$. All integers can be represented in the form $\frac{p}{q}$ where $q \neq 0$.

(v) Every rational number is an integer.

False, as rational numbers are of the form $\frac{p}{q}$ where $q \neq 0$. Integers are negative and positive numbers which are not in $\frac{p}{q}$ form.

For example, $\frac{1}{2}$ is a rational number but not an integer.

(vi) Every rational number is a whole number.

False, as rational numbers are of the form $\frac{p}{q}$ where $q \neq 0$. Whole numbers are natural numbers together with a zero. For example, $\frac{5}{7}$ is a rational number but not a whole number.