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

Given the relation schema $R(A, B, C, D, E)$ and functional dependencies:

1. $AB \rightarrow C$

2. $BC \rightarrow D$

3. $C \rightarrow E$

Attributes $A$ and $B$ do not appear on the right-hand side of any functional dependency, so every candidate key must contain both $A$ and $B$.

Let us find the attribute closure of $(AB)$:

• $(AB)^+ = \{A, B\}$

• Using $AB \rightarrow C \implies \{A, B, C\}$

• Using $BC \rightarrow D \implies \{A, B, C, D\}$

• Using $C \rightarrow E \implies \{A, B, C, D, E\}$

Since $(AB)^+$ contains all attributes of $R$, $AB$ is a candidate key. Since both $A$ and $B$ are essential, $AB$ is the only candidate key.

A superkey is any superset of a candidate key. Any subset of attributes containing $\{A, B\}$ is a superkey:

• The remaining attributes are $\{C, D, E\}$ (a set of $3$ attributes).

• The number of superkeys is $2^3 = 8$.

Therefore, the number of superkeys is 8.