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 show that integers are not commutative under subtraction :

a. 23 and -18

LHS -

23 - (-18)

=> 23 + 18

=> 43

[commutate the terms]

RHS -

-18 - 23

=> - 43

So,

LHS ≠ RHS

Hence, integers are not commutative under subtraction.

b. 38 and 54

LHS -

38 - 54

=> - 16

[commutate the terms]

RHS -

54 - 38

=> 16

So,

LHS ≠ RHS

hence, integers are not commutative under subtraction.

More to know :-

Commutative property :- It says that terms can commutate (change location) but the answer will never change. It is true for addition and multiplication only. It is not true for subtraction and division.

In algebraic form,

a + b = b + a

a × b = b × a

also,

a - b ≠ b - a

a ÷ b ≠ b ÷ a

Hope it helps.

#BeBrainly :-)