GATE CS 2014 Set 2 Q21 — Integrity Constraints

A superkey is a set of attributes that contains a candidate key.

For the given relation schema $R(E, F, G, H)$, the candidate key is $E$. Therefore, any superkey of $R$ must contain the attribute $E$.

The remaining attributes in the relation are $F$, $G$, and $H$. Each of these 3 attributes can either be included or excluded from the superkey:

• Attribute $F$: 2 choices (present or absent)
• Attribute $G$: 2 choices (present or absent)
• Attribute $H$: 2 choices (present or absent)

Thus, the total number of superkeys is given by:

The 8 superkeys are: $\{E\}$, $\{E, F\}$, $\{E, G\}$, $\{E, H\}$, $\{E, F, G\}$, $\{E, F, H\}$, $\{E, G, H\}$, and $\{E, F, G, H\}$.