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.
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
(i) True. Every natural number is a whole number because the set of natural numbers (typically starting from 1) is a subset of the whole numbers (starting from 0). This means that all natural numbers are included within the whole numbers.
(ii) False. Not every integer is a whole number. While whole numbers include all non-negative integers (0, 1, 2, 3, ...), integers also include negative numbers (-1, -2, -3, ...). Therefore, the negative integers are not considered whole numbers.
(iii) False. Every rational number is not necessarily a whole number. Rational numbers are numbers that can be expressed as the quotient or fraction (\frac{p}{q}) of two integers, where (p) (the numerator) and (q) (the denominator) are integers and (q \neq 0). While all whole numbers are rational (since they can be expressed as themselves over 1, such as (\frac{4}{1}) for the whole number 4), not all rational numbers are whole numbers because they can represent fractions (like (\frac{1}{2})) or even negative quantities (like (\frac{-4}{5})), which are not whole numbers.
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