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4. (4 points) Consider the relation RCA, B, C, D, E) with the set of FDs: F ABE, CD-E 4-+ C, C-+?). Decompose R into BCNF. Write and explain all steps in your decomposition.

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Answer #1

Answer)

R = (A,B,C,D,E)

FD's:

A,B --> E

C,D --> E

A --> C

C --> A

Step 1:

FD A,B --> E violates.

Table is split:

R1 = (A,B,E,C)

R2 =(A,B,D)

Step 2:

Checking whether R1 is in BCNF:

FD A --> C violates.

R3 = (A,C)

R4 = (A,B,E)

Step 3:

Checking whether R2 is in BCNF:

Yes, already in BCNF.

R3 and R4 are also in BCNF.

Thus:

R3 = (A,C)

R4 = (A,B,E)

R2 =(A,B,D)

are the final tables in BCNF.

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