Consider the relation X(P, Q, R, S, T, U) with the following set of functional…
2021
Consider the relation X(P, Q, R, S, T, U) with the following set of functional dependencies
F = {
{P, R} → {S, T};
{P, S, U} → {Q, R}
}
Which of the following is the trivial functional dependency in F⁺, where F⁺ is closure of F?
- A.
{P, R} → {S, T}
- B.
{P, R} → {R, T}
- C.
{P, S} → {S}
- D.
{P, S, U} → {Q}
- E.
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Correct answer: C
To find a trivial functional dependency in F⁺, recall that a functional dependency X → Y is trivial if Y ⊆ X. This means all attributes in the right-hand side (RHS) must be present in the left-hand side (LHS).
Now, evaluate each option:
{P, R} → {S, T}: S and T are not in {P, R}, so not trivial.
{P, R} → {R, T}: R is in LHS, but T is not, so not trivial.
{P, S} → {S}: S is in LHS, so RHS ⊆ LHS. This is trivial.
{P, S, U} → {Q}: Q is not in LHS, so not trivial.
Thus, the only trivial functional dependency among the options is {P, S} → {S}.