Normalization & Functional Dependencies

Consider a relational database schema with a relation $R(A, B, C, D)$. If $\{A, B\}$ and $\{A, C\}$ are the only two candidate keys of the relation $R$, then the number of superkeys of relation $R$ is ______. (*answer in integer*)

A functional dependency $F: X \to Y$ is termed as a *useful functional dependency* if and only if it satisfies all the following three conditions: • $X$ is not the empty set. • $Y$ is not the empty set. • Intersection of $X$ and $Y$ is the empty set. For a relation $R$ with 4 attributes, the total number of possible useful functional dependencies is __________

Consider a relation $R(A, B, C, D, E)$ with the following three functional dependencies. $$AB \to C;\quad BC \to D;\quad C \to E;$$ The number of superkeys in the relation R is __________

The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is _____.