Question

Explain by giving example - Properties of the group are not followed in subtraction of rational numbers.

Answer 1

Answer:

commutative

example- 1/2,1/4

1/2-1/4 ,1/4 -1/2

L.H.S

2/4-1/4=1/4

R.H.S

1/4-2/4=-1/4

1/4≠-1/4

therefore, LHS ≠RHS

Associative

example- 1/3,1/2,1/4

LHS

(1/3-1/2)-1/4

(4/12-6/12)-3/12

-2/12-3/12=5/12

RHS

1/3-(1/2-1/4)

4/12-3/12=1/12

5/12≠1/12

therefore, LHS ≠RHS