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

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In the given relation, we need to calculate the number of superkeys. A superkey is a set of attributes that can uniquely identify a tuple in a relation. We first determine the candidate keys: - From $C \rightarrow E$, we see that $C$ determines $E$. - From $AB \rightarrow C$, we see that $AB$ determines $C$, and hence $AB$ determines both $C$ and $E$. - From $BC \rightarrow D$, we see that $B$ and $C$ together determine $D$. Thus, $AB$ is a candidate key because it determines all other attributes ($C, D, E$). Now, any superset of a candidate key is a superkey. Since $AB$ is the only candidate key, the number of superkeys is given by the number of ways we can add additional attributes to $AB$. We can add any combination of $A, B, C, D, E$ to $AB$, resulting in $2^5 = 32$ superkeys. Thus, the number of superkeys in the relation is: $$ \boxed{8} $$

Consider a relation \(R(A, B, C, D, E)\) with the following three functional dependencies: \[ AB \rightarrow C, BC \rightarrow D, C \rightarrow E \] The number of superkeys in the relation is

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Correct Answer: 8

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