Question-18

Suppose the following functional dependencies hold on a relation \(U\) with attributes \(P, Q, R, S,\) and \(T\): - \(P \rightarrow QR\) - \(RS \rightarrow T\)

Which of the following functional dependencies can be inferred from the above functional dependencies?

• \(PS \rightarrow T\)
• \(R \rightarrow T\)
• \(P \rightarrow R\)
• \(PS \rightarrow Q\)

Answer

• \(PS \rightarrow T\)
• \(R \rightarrow T\)
• \(P \rightarrow R\)
• \(PS \rightarrow Q\)

Solution

Given FD set: - \(P \rightarrow QR\) - \(RS \rightarrow T\)

Inferring functional dependencies: - \((PS)^+ = \{PQRST\}\); Therefore, \(PS \rightarrow T\) can be inferred. - \((R)^+ = \{R\}\); \(R \rightarrow T\) cannot be inferred. - \((P)^+ = \{PQR\}\); Therefore, \(P \rightarrow R\) can be inferred. - \((PS)^+ = \{PQRST\}\); Therefore, \(PS \rightarrow Q\) can be inferred.

Hence, the inferred functional dependencies are \(PS \rightarrow T, P \rightarrow R,\) and \(PS \rightarrow Q\).