Question

If $a$ and $b$ are integers and $a\ne b$, then which of the following is INCORRECT?

• A. $a+b=b+a$
• B. $a-b=b-a$
• C. $a+0=0+a=a$
• D. $a-0=a\ne 0-a$

Answer 1

Answer: (B)

$a-b=b-a$

Option $B$ is correct

Given, $a$ and $b$ are integers and $a\ne b$.

$A)$ $a+b=b+a$

$\Rightarrow$It is true because of the commutative property

$\Rightarrow$Ex: If $a=2,b=3$ then $2+3=3+2=5$

$B)a-b=b-a$

$\Rightarrow$ $a-b=b-a$ is the incorrect statement in given options.

$\Rightarrow$ Because, we know value of $a$ and $b$ are not equal then $a-b$ and $b-a$ can not be equal.

$C)a+0=0+a=a$

$\Rightarrow$it is true beacuse of the identity property

$\Rightarrow$Ex: if $a=2$ then $2+0=0+2=2$

$D)a-0=a\ne 0-a$

$\Rightarrow$It is a false statement

$\Rightarrow$Ex: if $a=2$ then $2-0=2$ and $0-2=-2$

$\Rightarrow$clearly $2-0+2\ne 0-2$