Relation R=(E,F,G,H,I,J,K,L,M,N) has dependencies EF G, F IJ, EH KL, K M, L N. Find its key.

GATE 2014 CS (CS1) – Question 31

Databases · Integrity Constraints and Normal Forms · 1 mark · Multiple choice

Relation $R=(E,F,G,H,I,J,K,L,M,N)$ has dependencies $EF\to G$, $F\to IJ$, $EH\to KL$, $K\to M$, $L\to N$. Find its key.

$\{E,F\}$
$\{E,F,H\}$
$\{E,F,H,K,L\}$
$\{E\}$

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Correct answer: (B) $\{E,F,H\}$

Explanation

E,F,H do not appear on any dependency right-hand side, so each is required in every key. Their closure adds G viaEF, I,J viaF, K,L viaEH, then M viaK and N viaL. The closure contains every attribute, so **{E,F,H}, B** is the minimal key.