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 the natural numbers.

(ii) False; Integers are both positive and 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.