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KPGCET-CSE-2019-44

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The decomposition of a relation R of relational DBMS into two relations $RI(X)$ & $R2(Y)$ is lossless if

  1. $X \cap Y > X-Y \text{ or } X \cap Y > Y-X \text{ is in }F^+$
  2. $X – Y > X \cup Y \text{ or } Y – X > X \cup Y \text{ is in }F^+$
  3. $X \cap  Y > X – Y \text{ and } X \cap Y > Y – X \text{ are in }F^+$
  4. $X – Y > X \cup Y \text{ and } Y – X > X \cup Y \text{ are in }F^+$

Here $>$ means determines, $F^+$ is closure of functional dependencies and $X, \: Y$ are set of attributes present in $R1$ & $R2$  respectively. 

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