Let π,π,π and π be the attributes of a relation in a relational schema.β¦
2026
Let π,π,π and π be the attributes of a relation in a relational schema. Let π βΆπ indicate functional dependency in the context of a relational database, where X,Y β{π,π,π ,π}.
Which of the following options is/are always true?
- A.
If ( {π,π} βΆ{π } and {π} βΆ{π } ), then {π} βΆ{π }
- B.
If {π,π} βΆ{π }, then ( {π} βΆ{π } or {π} βΆ{π } )
- C.
If ( {π} βΆ{π } and {π} βΆ{π} ), then {π,π} βΆ{π ,π}
- D.
If {π} βΆ{π }, then {π,π} βΆ{π }
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Correct answer: C, D
Functional dependencies (FDs) define relationships where one set of attributes determines another in a relational schema.
The Union Rule states that if P βΆ R and Q βΆ S, then {P, Q} βΆ {R, S}. This validates Option C as always true.
The Augmentation Rule states that if P βΆ R, then {P, Q} βΆ {R, S}. Adding attributes to the determinant preserves the dependency, validating Option D.
Other options are incorrect because composite dependencies do not imply individual determinants without specific constraints.