=> for R1 : Given that a =(inverse of g)*b*g means a=b*e , and so a=b
(bcoz we know that (inverse of an element)*(element)=e ).
→ So statement boils down to R1: ∀a,b∈G,aR1b iff a=b
So if G={1,2} , Relation R1 = {(1,1),(2,2)} which is EQUIVALENCE RELATION.
=> for R2 : Given condition is that a = (inverse of b).
Again if G={1,2} , Relation R1 should contain atleast {(1,1),(2,2)} for it to be reflexive which is not always possible bcoz a != (inverse of a) for all ‘a’ . So can’t be reflexive, so can’t be equivalence.