This problem is actually of Regular language are closed under quotient operation .
means if we are having two language let as say L1 and L2 then if are suppose to do L1/L2 then = { x | where x,y belongs to L1 and Y belongs to L2 likewise L1/L2 = xy/y is actually right quotient (bydefault).
lets come to ur problem :
1. E*/L we are taking E(to represent sigma don't confuse) if E = {a,b} i am taking
here then E* = universal set so { ϵ, a,b,aa,ab,ba,bb.......}
and L let me take L={a}
so now E*/L = { ϵ, a,b,aa,ab,ba,bb.......}/a= ϵ/a U a/a U b/a U ab/a U ba/a U bb/a U aa/a ......... = Φ U ϵ U Φ U b U a ..... = E* so the first answer is totally right no doubt just see the proof given above.
2. L/E* = it will always derives prifix of L = prefix(L).
3. a* ba*/a* = the same u are goig to get just because if we are suppose to perform a*/a* = a*so no chages is going to happen in the answer so.
