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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.
To find:
We need to check whether the given statements are true or false.
Solution:
We know that,
Whole Numbers:
Whole numbers are 0, 1, 2, 3,......, and so on.
Natural Numbers:
Natural numbers are 1, 2, 3, 4, 5.....and so on.
Therefore, every natural number is a whole number.
Integers:
Integers are like whole numbers, but they also include negative numbers.
• It includes negative numbers $(-1, -2, -3, -4, ………)$
• It includes positive numbers $(1, 2, 3, 4, 5, ………)$
• It includes Zero
• Decimal numbers and fractions are not included in integers.
Rational Numbers:
A number that can be expressed in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q$ is not equal to zero is a rational number.
Rational numbers like $\frac{5}{2}$, $\frac{-10}{3}$ are not whole numbers.
Therefore,
(a) The given statement is true.
(b) The given statement is false.
(c) The given statement is false.
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