Question

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

(i) Every natural number is a whole number. 

(ii) Every integer is a whole number. 

(iii) Every rational number is a whole number

Answer 1

(i) True; since the collection of whole numbers contains all natural numbers.
(ii) False; as integers may be negative but whole numbers are positive. For example: −3 is an integer but not a whole number.
(iii) False; as rational numbers may be fractional but whole numbers may not be. 

For example: \(\frac{1}{5}\) is a rational number but not a whole number.