Question:

Published on: 3 August, 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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