Question 50

Given functional dependencies:

1. $P \to QR$
2. $RS \to T$

Check each candidate functional dependency using attribute closure:

• Option A ($PS \to T$):
  Start with $\{P, S\}$.
  Since $P \to QR$, add $Q$ and $R$: $\{P, Q, R, S\}$.
  Since $RS \to T$, and both $R, S \in \{P, Q, R, S\}$, add $T$: $\{P, Q, R, S, T\}$.
  Since $T \in (PS)^+$, $PS \to T$ can be inferred. Option A is correct.

• Option B ($R \to T$):
  Start with $\{R\}$. Neither dependency applies since neither $P$ nor $RS$ is a subset of $\{R\}$.
  Thus $R^+ = \{R\}$. Since $T \notin R^+$, $R \to T$ cannot be inferred. Option B is incorrect.

• Option C ($P \to R$):
  Start with $\{P\}$. By dependency 1, $P \to QR$, which by the decomposition rule implies $P \to Q$ and $P \to R$. Thus $R \in P^+$, so $P \to R$ can be inferred. Option C is correct.

• Option D ($PS \to Q$):
  From closure $(PS)^+ = \{P, Q, R, S, T\}$, $Q \in (PS)^+$. Thus $PS \to Q$ can be inferred. Option D is correct.