Question

If a and b are two whole numbers, then commutative law is applicable to subtraction if and only if

• A. $a=b$
• B. a $\ne$ b
• C. $a>b$
• D. $a<b$

Answer 1

Answer: (A)

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.

Now, if $a=b=3$ then, $a-b=3-3=0$ which is also a whole number.

Hence, whole numbers are commutative under subtraction if and only if $a=b$.