Question

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

(i) Every natural number is a whole number. [1 mark]
(ii) Every integer is a whole number. [1 mark]
(iii) Every rational number is a whole number. [1 mark]

Answer 1

(i) True.
Since the natural numbers are a subset of whole numbers.
Whole numbers are 0, 1, 2, ...
Natural numbers are 1, 2, 3, ...
(1 mark)
(ii) False.
An integer can either be negative or positive but whole numbers are always non negative.
-1 is an integer but not a whole number.
(1 mark)
(iii) False.

Rational numbers may be fractional but whole numbers are not.
For example, $\frac{1}{2}$ is a rational number but not a whole number.
(1 mark)