Are the following statements true or false? Give reasons for your answer? Every whole number is a natural number Every integer is a rational number. Every rational number is an integer. Every natural number is a whole number. Every integer is a whole number Every rational number is a whole number

Explanation

(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: `1/2, 2/3, -3/2` etc. `-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'.
Integers:
(All numbers both negative and positive) ....,`-3,-2,-1,0,1,2,3`,....
here, Fraction like `3/2, 1/2`, 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: `1/2, 2/3` etc
Whole numbers:
(All numbers starting from 0 )`0,1,2,3,4,5`,....
Fractions like
`3/5, 1/2` etc are not whole numbers but are rational numbers. Hence, False.