Let 𝑃,𝑄,𝑅 and 𝑆 be the attributes of a relation in a relational schema.…

2026

Let 𝑃,𝑄,𝑅 and 𝑆 be the attributes of a relation in a relational schema. Let 𝑋 βŸΆπ‘Œ indicate functional dependency in the context of a relational database, where X,Y βŠ†{𝑃,𝑄,𝑅,𝑆}.

Which of the following options is/are always true?

  1. A.

    If ( {𝑃,𝑄} ⟢{𝑅} and {𝑃} ⟢{𝑅} ), then {𝑄} ⟢{𝑅}

  2. B.

    If {𝑃,𝑄} ⟢{𝑅}, then ( {𝑃} ⟢{𝑅} or {𝑄} ⟢{𝑅} )

  3. C.

    If ( {𝑃} ⟢{𝑅} and {𝑄} ⟢{𝑆} ), then {𝑃,𝑄} ⟢{𝑅,𝑆}

  4. D.

    If {𝑃} ⟢{𝑅}, then {𝑃,𝑄} ⟢{𝑅}

Attempted by 54 students.

Show answer & explanation

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 ⟢ R and Q ⟢ S, then {P, Q} ⟢ {R, S}. This validates Option C as always true.

The Augmentation Rule states that if P ⟢ R, then {P, Q} ⟢ {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.

Explore the full course: Gate Guidance By Sanchit Sir