Question

Which of the following properties does not hold for subtraction in integers?

• A. Closure
• B. Commutative
• C. Identity element
• D. Property of zero

Answer 1

The correct option is B

Commutative

Correct option: b) Commutative

Let $a=2andb=4$ be two integers then,

$a-b=2-4=-2$ and$b-a=4-2=2$

So, $a-b\ne b-a$

Hence, the subtraction of integers is not commutative.

Incorrect options:

a) Closure

Let $a=2andb=4$ be two integers then, $a-b=2-4=-2$

$-2$ is also an integer.

So, subtraction is closed under integers.

c) Identity element

For any integer$a=2$, we have

$$\begin{gathered} a-0=2-0 \\ =2=a \end{gathered}$$

Here$0$ is the identity element.

d) Property of zero

When zero is subtracted from the integer, the difference is the integer itself.

For any integer$a=2$, we have

$$\begin{gathered} a-0=2-0 \\ =2=a \end{gathered}$$

So, it holds the property of zero.

Hence, option (b) is correct.