Consider a relation schema R = (A, B, C, D, E, F) on which the following functional dependencies hold :

A → B B, C → D

E → C

D → A What are the candidate keys of R?

1. AAE and BE
2. BAE, BE, and DE
3. CAEF, BEF and BCF
4. DAEF, BEF and DEF

Pick an option to check yourself, or open the answer below.

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Correct answer: D. AEF, BEF and DEF

Explanation

E and F never appear on a right side, so every key contains EF; E gives C. AEF: A → B, BC → D gives all. BEF: BC → D → A. DEF: D → A → B. So AEF, BEF and DEF.