Assume there is an index on attribute R.a. Describe how this index could be used to improve the execution of the following operations. Under what circumstances would be index-based algorithm be more efficient than sort- or hash-based algorithms? R U_s S (assume that R and S have no duplicates, although they may have tuples in common? R Intersection_s S (again with R and S sets? delta (R)? Assume there is an index on attribute R.a. Describe how this index could be used to improve the execution of the following operations. Under what circumstances would be index-based algorithm be more efficient than sort- or hash-based algorithms? R U_s S (assume that R and S have no duplicates, although they may have tuples in common? R Intersection_s S (again with R and S sets? delta (R)