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.
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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