Question

Subtraction of integers is
(a) commutative but no associative
(b) commutative and associative
(c) associative but not commutative
(d) neither commutative nor associative

Answer 1

(d) neither commutative nor associative

Subtraction of integers is not commutative
For example: If a = 1 and b = 2, then both are integers

$$\begin{gathered} 1-2=-1 \\ 2-1=1 \end{gathered}$$
$\Rightarrow -1\ne 1$
$\therefore a-b\ne b-a\forall a,b\in Z$

Subtraction of integers is not associative.
For example: If a = 1, b = 2, c = 3, then all are integers

$$\begin{gathered} 1-\left(2-3\right)=1+1 \\ =2 \\ \left(1-2\right)-3=-1-3 \\ =-4 \\ \Rightarrow 2\ne -4 \\ \therefore a-\left(b-c\right)\ne \left(a-b\right)-c,\forall a,b,c\in Z \end{gathered}$$