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.
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.
(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 
)
where both p and q are integers,
.
Eg: 
-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 
)
where both p and q are integer ,
.
Eg: 
Integers:
(All numbers both negative and positive)
.......,-3,-2,-1,0,1,2,3,....
here, Fraction like 
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 
)
where both p and q are integer ,
.
Eg: 
Whole numbers:
(All numbers starting from 0 )
0,1,2,3,4,5,....
Fractions like
(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 )
where both p and q are integers, .
Eg:
-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 )
where both p and q are integer , .
Eg:
Integers:
(All numbers both negative and positive)
.......,-3,-2,-1,0,1,2,3,....
here, Fraction like 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 )
where both p and q are integer , .
Eg:
Whole numbers:
(All numbers starting from 0 )
0,1,2,3,4,5,....
Fractions like
