Given the relation schema FLIGHT (Gate#, Flight#, Date, Airport, Aircraft, Pilot) and the constraint set F {fd1, fd2, fd3} where:
fd1: {Airport, Flight#, Date}  Gate
fd2: {Flight#, Date}  Aircraft
fd3: {Flight, Date}  Pilot
a. List the candidate key(s) of FLIGHT.
b. For each candidate key, indicate the immediate normal form violated in FLIGHT by each of the functional dependencies given above.
c. If FLIGHT is not in BCNF, design a relational schema that:
• is in BCNF, and
• yields a lossless-join decomposition
d. Are all functional dependencies in F preserved? If not, which are not preserved?