Given a relation schema R = (A,B,C,D,E,F,G), and a set of functional dependencies FD = {A -> BCDEFG, CE -> A, BF -> EG } held on R.

1. (3 points) {CE} a candidate key of relation R? Justify your answer.
2. (3 points) Is R in BCNF? If not, decompose it into smaller relations such that these smaller relations are in BCNF?
3. (2 points) Is the decomposition a lossless-join decomposition? Justify your answer.