Question:

Published on: 23 January, 2022

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 AD→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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