The GATE Grind

GATE 2019 CS – Question 42

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

Let the set of functional dependencies $F=\{QR\to S,\ R\to P,\ S\to Q\}$ hold on a relation schema $X=(PQRS)$. $X$ is not in BCNF. Suppose $X$ is decomposed into two schemas $Y$ and $Z$, where $Y=(PR)$ and $Z=(QRS)$.

Consider the two statements given below.

I. Both $Y$ and $Z$ are in BCNF

II. Decomposition of $X$ into $Y$ and $Z$ is dependency preserving and lossless

Which of the above statements is/are correct?

  1. Both I and II
  2. I only
  3. II only
  4. Neither I nor II

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) II only

Explanation

$Y=(PR)$ with $R\to P$ is in BCNF, but in $Z=(QRS)$ the FD $S\to Q$ has a non-key determinant ($S$ is not a key), so $Z$ is not in BCNF and I is false. The common attribute $R$ is a key of $Y$, so the decomposition is lossless, and the FDs $QR\to S$, $R\to P$, $S\to Q$ are all preserved within $Y$ and $Z$, so II is true.