## Let us have a look at the properties of whole numbers under subtraction:

(i)Β Closure property :Β If $a$ and $b$ are two whole numbers such that $a>b$ or $a=b$, then $aβb$ is a whole number. If $a<b$, then subtraction $aβb$ is not possible in whole numbers. For example: If $a=3$ and $b=5$ then,

$3β5=β2$ which is not a whole number.

Therefore,Β whole numbers are not closed underΒ subtraction.

(ii)Β Commutative property :Β The subtraction of whole numbers is not commutative, that is, if $a$ and $b$ are two whole numbers, then in general $aβb$ is not equal to $(bβa)$.

Verification:

We know that $9β5=4$ but $5β9=β4$ which is not a whole number. Thus, for two whole numbers $a$ and $b$ if $a>b$, then $aβb$ is a whole number but $bβa$ is not possible and if $b>a$, then $bβa$ is a whole number but $aβb$ is not possible.

Therefore,Β whole numbers are not commutative underΒ subtraction.

(iii)Β Associative of addition :Β The subtraction of whole numbers is not associative. That is, if $a,b,c$ are three whole numbers, then in general $aβ(bβc)$ is not equal to $(aβb)βc$.

Verification:

We have,

$20β(15β3)=20β12=8$,

and, $(20β15)β3=5β3=2$

So, $20β(15β3)ξ=(20β15)β3$.

Therefore,Β whole numbers are not associativeΒ underΒ subtraction.

Hence, all of the properties are not applicable toΒ subtractionΒ of whole numbers.