5. Find a minimal basis for the following set F of functional dependencies. Show your work. (Answers that show only the final result without showing the steps taken to obtain it will receive no credit.)

U,W -> X

W -> U,Y

W,Z -> Y

Y ->X

6. Consider the universal relation

STUDENT(StuID, SSNum, FName, LName, Major, Dept, Group)

with the following set F of functional dependencies:

StuID -> SSNum, Major

SSNum -> FName, LName,

StuID StuID -> Dept

Major -> Dept

FName -> Group

a. Identify all of the candidate keys of F.

b. Construct a decomposition of EMPLOYEE into relations in 3NF that has both the dependency preservation property and the lossless join property. Use the algorithm discussed in class, and show your work. (Answers that show only the final result without showing the steps taken to obtain it will receive no credit.)

(Hint: I will tell you that if you split StuID -> SSNum, Major into two functional dependencies, split SSNum -> FName, LName, SID into three functional dependencies, and remove StuID -> Dept, then the resulting set is a minimal basis of F.)