Suppose that we are given a relation schema r with four attributes, abcd, and the set of fds f = { ab  c, bc  d, d  a }. assuming those are the only dependencies that hold for r, answer the following questions (justify briefly your answers): (a) is ac a key of r? (b) is ab a key of r? (c) what is a prime attribute? is attribute a a prime attribute? (d) is r in 3rd normal form (3nf)? (e) is r in boyce-codd normal form (bcnf)