Let G a epsilon R 1 SolutionGiven a b ab 1ab here a is

Solution

Given a * b = a+b/ (1+ab)

here a is in between -1 and 1

and G depends on a

(G,*) is

initially taking a=-1

-1 * b = ( -1 + b) / ( 1 - b)

-b = b - 1 / 1 -b

taking a=1

b = 1+b/ 1+b

where b=1

now taking (R,+)

R is an real number between -1 and 1

taking R= -1 and R=1

initially taking a=-1

-1 * b = ( -1 + b) / ( 1 - b)

-b = b - 1 / 1 -b

taking a=1

b = 1+b/ 1+b

where b=1

we obtain the same answer as above

so (G , *) = (R,+)