UGC NET CSE | December 2018 | Part 2 | Question: 82

Question

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

• $A \rightarrow B$
• $B, C \rightarrow  D$
• $E \rightarrow  C$
• $D \rightarrow  A$

What are the candidate keys of $R$ ?

• A. $AE$ and $BE$
• B. $AE, BE$ and $DE$
• C. $AEF, BEF$ and $BCF$
• D. $AEF, BEF$ and $DEF$

Answer 1

$(AEF)^+=\left\{A,E,B,C,D,F \right \}$

$(BEF)^+=\left\{B,E,C,D,A,F \right \}$

$(DEF)^+=\left\{D,E,C,A,B,F\right \}$

$AEF,BEF,DEF$ are the minimal superkeys.

So, $(D)$ should be the answer