The GATE Grind

GATE 2024 CS (CS1) – Question 44

Databases · Integrity Constraints and Normal Forms · 2 marks · Multiple select

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

  1. $(X,Y)\to(Z,W)$ implies $X\to(Z,W)$
  2. $(X,Y)\to(Z,W)$ implies $(X,Y)\to Z$
  3. $((X,Y)\to Z$ and $W\to Y)$ implies $(X,W)\to Z$
  4. $(X\to Y$ and $Y\to Z)$ implies $X\to Z$

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Show answer and explanation

Correct answer: (B) $(X,Y)\to(Z,W)$ implies $(X,Y)\to Z$; (C) $((X,Y)\to Z$ and $W\to Y)$ implies $(X,W)\to Z$; (D) $(X\to Y$ and $Y\to Z)$ implies $X\to Z$

Explanation

B follows by decomposition. C: W→Y gives (X,W)→(X,Y)→Z by augmentation and transitivity. D is transitivity. A is false since dropping Y from the determinant is not implied.