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Question

State whether the following statements are true or false. Give reasons for your answer.

(i) Every natural number is a whole number.

(ii) Every whole number is a natural number.

(iii) Every integer is a whole number.

(iv) Every integer is a rational number.

(v) Every rational number is an integer.

(vi) Every rational number is a whole number.


Solution

(i) Every natural number is a whole number.

Natural number:
(All numbers starting from 1)
1,2,3,4,5,....

Whole numbers:
(All numbers starting from 0 )
0,1,2,3,4,5,....

1,2,3,4,5,.... are both natural as well as whole numbers.
thus, All natural numbers are the whole numbers.  

so, True

(ii)Every whole number is a natural number.

Natural number:
(All numbers starting from 1)
1,2,3,4,5,....

Whole numbers:
(All numbers starting from 0 )
0,1,2,3,4,5,....

Here, we can see Zero is a whole number but not a natural number.

so, It is False


(iii) Every integer is a whole number.

Integers:
(All numbers both negative and positive)
.......,-3,-2,-1,0,1,2,3,....

Whole numbers:
(All numbers starting from 0 )
0,1,2,3,4,5,....

As integers may be negative but whole numbers are positive.
Eg: -3 is an integer but not whole number

so, False


(iv) Every integer is a rational number.

Integers:
(All numbers both negative and positive)
.......,-3,-2,-1,0,1,2,3,....

Rational number:
(All numbers in the form of  p over q )
where both p and q are integers,q not equal to 0 .

Eg: 1 half comma 2 over 3 comma negative 3 over 2 comma 3 comma negative 2 space e t c


-3,-2,-1,0,1,2,3 are both Integers as well as rational numbers,
thus, Every integer is a rational number.
so, True

(v) Every rational number is an integer.

Rational number:
(All numbers in the form of  p over q )
where both p and q are integer ,q not equal to 0 .

Eg: 1 half comma 2 over 3 comma negative 3 over 2 comma 3 comma negative 2 space e t c


Integers:
(All numbers both negative and positive)
.......,-3,-2,-1,0,1,2,3,....

here,  Fraction like 3 over 2 comma 1 half comma e t c are Rational Number but not Integers.
So,  Statement is False

(vi) Every rational number is a whole number.

Rational number:
(All numbers in the form of  p over q )
where both p and q are integer ,q not equal to 0 .

Eg: 1 half comma 2 over 3 comma negative 3 over 2 comma 3 comma negative 2 space e t c


Whole numbers:
(All numbers starting from 0 )
0,1,2,3,4,5,....

Fractions like

 3 over 5 comma 1 half space e t c space a r e space n o t space w h o l e space n u m b e r s space b u t space a r e space r a t i o n a l space n u m b e r s space h e n c e space bold italic F bold italic a bold italic l bold italic s bold italic e



 


Mathematics
Secondary School Mathematics IX
Standard IX

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