Alternatively, you could have started with the bcnf algorithm and checked for dependency preservation.

Let R=(A,B,C,D,E,G) and let F be{A→BDG, BG→DE, B→D, D→A}. Find a good design that takes into account our design criteria and justify your design. [ To approach the problem, first aim for 3NF and then seek BCNF if possible. Alternatively, you could have started with the BCNF algorithm and checked for dependency preservation. ]