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.
(i) True, since the collection of whole numbers contains all natural numbers.
(ii) False, for example, - 2 is an integer but not a whole number.
(iii) False, for example, is a rational number but not a whole number.
State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form where m is a natural number.
(iii) Every real number is an irrational number.
(i) True, since collection of real numbers is made up of rational and irrational numbers.
(ii) False, because no negative number can be the square root of any natural number.
(iii) False, for example, 2 is real but not irrational.