Given the relational schema R = (U, V, W, X, Y, Z) and the set of functional dependencies: \U V,\ U W,\ WX Y,\ WX Z,\ V X\ Which of the following functional dependencies can be derived from the above set?

GATE DA 2024 Q46: Functional dependencies derivable from a given set

Given the relational schema $R = (U, V, W, X, Y, Z)$ and the set of functional dependencies:

$\{U \to V,\ U \to W,\ WX \to Y,\ WX \to Z,\ V \to X\}$

Which of the following functional dependencies can be derived from the above set?

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Answer: A, B, D (official GATE 2024 final answer key)

Concept used: Attribute closure: $\alpha \to \beta$ holds exactly when $\beta \subseteq \alpha^+$ .

First step: $(VW)^+$ : $V \to X$ adds $X$ , then $WX \to Y, Z$ , giving $VWXYZ$ (no $U$ ).

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key