Question-14

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 super keys in the relation \(R\) is _________.

Answer

\(8\)

Solution

Given functional dependencies: \(AB \rightarrow C\), \(BC \rightarrow D\), \(C \rightarrow E\)

1. Candidate Key: \(AB\)
2. Candidate Key Combinations with non-prime attributes:
   • Combinations with the remaining attributes \((n - 2)\) where \(n\) is the number of Attributes
   • Total number of super keys with combinations: \(2^{5-2} = 2^3 = 8\)

Therefore, there are 8 super keys for the relation \(R\), which are: {AB, ABC, ABD, ABE, ABCD, ABDE, ABCE, ABCDE}