Suppose the following functional dependencies hold on a relation $U$ with attributes $P, Q, R, S$, and $T$: $$\begin{aligned} P &\rightarrow QR RS &\rightarrow T \end{aligned}$$ Which of the following functional dependencies can be inferred from the above functional dependencies?

To check which functional dependencies (FDs) $X \rightarrow Y$ can be inferred, we compute the attribute closure $X^+$ with respect to the given set of FDs:

1. Check $PS \rightarrow T$ and $PS \rightarrow Q$ (Options A and D):

   • Initial closure: $(PS)^+ = \{P, S\}$

   • Applying $P \rightarrow QR$: $(PS)^+ = \{P, Q, R, S\}$

   • Applying $RS \rightarrow T$: since $\{R, S\} \subseteq (PS)^+$, we add $T$, giving $(PS)^+ = \{P, Q, R, S, T\}$

   • Since $T \in (PS)^+$, $PS \rightarrow T$ holds (Option A is correct).

   • Since $Q \in (PS)^+$, $PS \rightarrow Q$ holds (Option D is correct).

2. Check $R \rightarrow T$ (Option B):

   • Initial closure: $R^+ = \{R\}$

   • No functional dependency can be applied since $RS \rightarrow T$ requires both $R$ and $S$.

   • Thus, $R^+ = \{R\}$. Since $T \notin R^+$, $R \rightarrow T$ cannot be inferred (Option B is incorrect).

3. Check $P \rightarrow R$ (Option C):

   • From $P \rightarrow QR$, by Armstrong's Decomposition Rule (or using $P^+ = \{P, Q, R\}$), $P \rightarrow R$ holds (Option C is correct).

Therefore, the correct options are A, C, and D.