R(UVWXYZ)
Which FD can be determined from the above FD Set?
Which FD can be determined from the above FD Set?
Solution and Explanation
VW→Y; VW→YZ; WX→YZ
Top Questions on Functional Dependency
Let 𝑃, 𝑄, 𝑅 and 𝑆 be the attributes of a relation in a relational schema. Let 𝑋 ⟶𝑌
indicate functional dependency in the context of a relational database, where
𝑋, 𝑌 ⊆{𝑃, 𝑄, 𝑅, 𝑆}.
Which of the following options is/are always true?- GATE CS - 2026
- Computer Science and IT Engineering
- Functional Dependency
In the context of schema normalization in relational DBMS, consider a set F of
functional dependencies. The set of all functional dependencies implied by F is
called the closure of F. To compute the closure of F, Armstrong’s Axioms can be
applied. Consider 𝑋, 𝑌, and 𝑍 as sets of attributes over a relational schema. The three
rules of Armstrong’s Axioms are described as follows.
Reflexivity: If 𝑌⊆𝑋 , then 𝑋→𝑌
Augmentation: If 𝑋→𝑌, then 𝑋𝑍→𝑌𝑍 for any Z
Transitivity: If 𝑋→𝑌 and 𝑌→𝑍, then 𝑋→𝑍
The additional rule of Union is defined as follows.
Union: If 𝑋→𝑌 and 𝑋→𝑍, then 𝑋→𝑌𝑍
It can be proved that the additional rule of Union is also implied by the three rules
of Armstrong’s Axioms. Listed below are four combinations of these three rules.
Which one of these combinations is both necessary and sufficient for the proof ?- GATE CS - 2026
- Computer Science and IT Engineering
- Functional Dependency
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