Question

1 ; With the help of a suitable example show that the subtraction is non commutative and non-associative for integer​

Answer 1

Step-by-step explanation:

1. To prove that subtraction is non commutative for integer. Commutative property says that integers can be subtracted in any order but this is not true. The below example shows that subtraction is non commutative for subtraction:

To prove (a-b $\neq$  b-a)

Let a=1, b= -2

LHS : 1- (-2)

= 1+2 = 3

RHS : -2-1

= -3

3 $\neq$ -3

LHS $\neq$ RHS

Hence proved.

2. To prove that subtraction is non associactive for integers. Associative property says that the bracket's order can be changed, but it is not true in case of subtraction. The below example shows that subtraction is non associative for subtraction.

To prove- (a-b)-c $\neq$ a- (b-c)

Let a=1, b=2, c=-1

LHS : (1-2)-(-1)

= -1+1

=0

RHS : 1 - (2-(-1))

=1-(2+1)

=1-3

= -2

0$\neq$ -2

LHS $\neq$ RHS

Hence Proved.

Hope it helps...

Answer 2

Answer:

For example, if we take 3-2 then we have to change it to 2-3. 3-2=1 but 2-3=(-1) so subtraction is non commitative

hope it helps...be happy...

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