Question

1 . 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

✯✯ QUESTION ✯✯

1 . 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.

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✰✰ ANSWER ✰✰

( i ) True

Because Collection of whole numbers contains all the natural numbers ..

( ii ) False

For Example , -6 , -78 etc.. are not whole numbers..

( iii ) False

For Example , $\dfrac{1}{2}$ is a rational number but not a whole number..

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✔Definitions : -

★Rational Numbers : -

The numbers that can be written in the form of $\dfrac{p}{q}$ where p and q are integers and q≠0..

For Example :. 2/6 ,7/10 etc....

★Irrational Numbers : -

The numbers that can not be written in the form of $\dfrac{p}{q}$ where p and q are integers and q≠0..

For Example :. 0.1212..,45.345345...etc..

★Integers : -

All Negative numbers , all positive numbers with zero form Integers..

For Example :. -4 , 0 , 89....etc..

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Answer 2

(i) Every natural number is a whole number.

True

Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)

i.e., Natural numbers= 1,2,3,4…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3…

Or, we can say that whole numbers have all the elements of natural numbers and zero.

Every natural number is a whole number; however, every whole number is not a natural number.

(ii) Every integer is a whole number.

False

Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.

i.e., integers= {…-4,-3,-2,-1,0,1,2,3,4…}

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers include whole numbers as well as negative numbers.

Every whole number is an integer; however, every integer is not a whole number.

(iii) Every rational number is a whole number.

Solution:

False

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0.

i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers includes whole numbers as well as negative numbers.

Every whole numbers are rational, however, every rational numbers are not whole numbers.