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49 votes
49 votes

Consider the relation $X(P,Q,R,S,T,U)$ with the following set of functional dependencies

$F = \{ \\ \; \; \{P, R\} \rightarrow \{S, T\}, \\ \; \; \{P, S, U\} \rightarrow \{Q, R\} \\ \; \}$

Which of the following is the trivial functional dependency in $F^+$, where $F^+$ is closure to F?

  1. $\{P, R\} \rightarrow \{S, T\}$
  2. $\{P, R\} \rightarrow \{R, T\}$
  3. $\{P, S\} \rightarrow \{S\}$
  4. $\{P, S, U\} \rightarrow \{Q\}$

1 Answer

Best answer
68 votes
68 votes

Option C is correct because $\{P,S\}→\{S\}$
for trivial FD, if $X→Y$ then $Y$ must be a subset of $X$ and for non trivial FD $X ∩ Y= \emptyset$.  and here $\{S\}$ is subset of $\{P,S\}$.

PS: Trivial means something which is always there. An attribute set always determines any of the component attributes and this is always true irrespective of the relation instance. Hence, this $FD$ becomes trivial.

edited by
1 flag:
✌ Edit necessary (Deepak Poonia “Definition of Non-trivial FD is wrong.”)
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