Question

Write, whether the given statement is true or false. Give reasons.
(i) Every natural number is a whole number.
(ii) Every whole number is a natural number.
(iii) Every integer is a rational number.
(iv) Every rational number is a whole number.
(v) Every terminating decimal is a rational number.
(vi) 0 is a rational number.

Answer 1

(i) True
Natural numbers start from 1 to infinity and whole numbers start from 0 to infinity; hence, every natural number is a whole number.

(ii) False
0 is a whole number but not a natural number, so every whole number is not a natural number.

(iii) True
Every integer can be expressed in the $\frac{p}{q}$ form.

(iv) False
Because whole numbers consist only of numbers of the form $\frac{p}{1}$, where p is a positive number. On the other hand, rational numbers are the numbers whose denominator can be anything except 0.

(v) True
Every terminating decimal can be easily expressed in the $\frac{p}{q}$ form.

(vi) True
Every terminating decimal can be easily expressed in the $\frac{p}{q}$ form.

(vii) True
0 can be expressed in the form $\frac{p}{q}$, so it is a rational number.