Suppose the following functional dependencies hold on a relation U with attributes P, Q, R, S, and T: P QR RS T Which of the following functional dependencies can be inferred from the above functional dependencies?

GATE CSE 2021 Set 2 Q50: FDs implied by P → QR and RS → T

Suppose the following functional dependencies hold on a relation U with attributes $P$ , $Q$ , $R$ , $S$ , and $T$ :

$P \rightarrow QR \qquad RS \rightarrow T$

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

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Answer: A, C, D (official GATE 2021 final answer key)

Concept used: An FD $X \rightarrow Y$ follows exactly when $Y \subseteq X^+$ .

First step: Compute $PS^+ = \{P, S, Q, R, T\}$ , $P^+ = \{P, Q, R\}$ and $R^+ = \{R\}$ .

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key