GATE 2024 DA – Question 46

Database Management and Warehousing · Integrity constraints and normal forms · 2 marks · Multiple select

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?

$VW \to YZ$
$WX \to YZ$
$VW \to U$
$VW \to Y$

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Correct answer: (A) $VW \to YZ$; (B) $WX \to YZ$; (D) $VW \to Y$

Explanation

From $WX \to Y$ and $WX \to Z$ we get $WX \to YZ$ (B). Since $V \to X$, we have $VW \to WX$ by augmentation with $W$, and then $VW \to YZ$ by transitivity (A). From $VW \to YZ$ we get $VW \to Y$ (D). Nothing determines $U$ from $V$ and $W$: the closure of $VW$ is $\{V, W, X, Y, Z\}$, which does not contain $U$, so C cannot be derived.