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Question:
Published on: 25 April, 2024

Let R (ABCDE) be a relation schema and consider the following functional dependencies F = { AB→ E, AD→B, B→ C, C →D}. Find out the candidate key.

Answer:

Case 1: as B→C and C →D, so                            B→D (transitivity)

                       as B→D so                                AB→AD (augmentation)

                       as AB→E so                              AB→ABE (reflexivity)

                       as AB→ABE, AND AB→AD so      AB→ABCDE(union)

            So the closure of AB is . so, AB is a candidate key.

Case 2: as AD→B so                                         AD→ABD (reflexivity)

            as AB→E so                                         ABD→DE (augmentation)

            as AD→B and B→C so                           ADrarr;C (transitivity)

            as AD→ABD, AD→C and AD→DE so        AD→ABCDE (union)

            So the closure of AB is . so, AD is also a candidate key.

 

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