Question

Which of the following properties are not applicable to the subtraction of whole numbers?

• A. Closure property
• B. Commutative property
• C. Associative proptery
• D. All the above

Answer 1

Answer: (D)

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

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

$3-5=-2$ which is not a whole number.

Therefore, whole numbers are not closed under subtraction.

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

Verification:

We know that $9–5=4$ but $5–9=-4$ which is not a whole number. Thus, for two whole numbers $a$ and $b$ if $a>b$, then $a–b$ is a whole number but $b–a$ is not possible and if $b>a$, then $b–a$ is a whole number but $a–b$ is not possible.

Therefore, whole numbers are not commutative under subtraction.

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

Verification:

We have,

$20–(15–3)=20–12=8$,

and, $(20–15)–3=5–3=2$

So, $20–(15–3)\ne (20–15)–3$.

Therefore, whole numbers are not associative under subtraction.

Hence, all of the properties are not applicable to subtraction of whole numbers.