Question

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

​

Answer 1

Solution:

___________________

If x,y €Z , then

x-y = y-x

( commutative Property )

___________________

a ) x = 23 , y = -18

x-y

= 23-(-18)

= 23+18

= 41 ---(1)

y-x

= -18-23

= -41 ----(2)

Therefore,

41 ≠ -41

x-y ≠ y-x

ii) Here , x=38, y = 54

x-y

= 38-54

= -16

y-x

= 54-38

= 16

Therefore,

-16 ≠ 16

x-y ≠ y-x

We conclude that,

Integers are not commutative

under subtraction.

•••••

Answer 2

Answer:

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Step-by-step explanation:

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