Question

Give a counterexample to show that integers are not commutative under subtraction using: a. 23 and -18 b. 38 and 54​

Answer 1

To prove that integers are not commutative under subtraction :

a. 23 & (-18)

→

LHS -

23 - (-18)

=> 23 + 18

=> 41

[Now commutate the terms]

RHS -

(-18) - 23

=> -18 - 23

=> - 41

So,

LHS ≠ RHS

hence, It is proved Integers are not commutative under subtraction.

b. 38 & 54

→

LHS -

38 - 54

=> - 16

[Now, commutate the terms]

RHS -

54 - 38

=> 16

=> LHS ≠ RHS

Hence, integers are not commutative under subtraction.

More to know :-

Commutative property :- commutative property says that terms commutate (change their location) but the answer will not change. It is true for only addition and multiplication, not for subtraction and division.

In algebraic form,

a + b = b + a

a × b = a × b

and

a - b ≠ b - a

a ÷ b ≠ b - a

hope it helps.

#BeBrainly :)