Functional dependencies on relation U(P,Q,R,S,T): P -- QR and RS -- T. Which of the following FDs

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2021 GATE-CS Database Management Systems paper.

Q: How can I prepare for GATE-CS Database Management Systems?

To prepare for GATE-CS Database Management Systems, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2021 question covers Normal Forms (1NF, 2NF, 3NF, BCNF) topic.

Q: What is the difficulty level of this question?

This GATE-CS 2021 Database Management Systems question has a medium difficulty level and is marked as an important question.

Q: Where can I find more GATE-CS previous year questions?

You can find more GATE-CS previous year questions on AspirantMitraa. Browse by subject, topic, year, and difficulty level to practice effectively.

Question

Functional dependencies on relation U(P,Q,R,S,T): P --> QR and RS --> T. Which of the following FDs can be inferred?(A) P --> R(B) PS --> T(C) PS --> Q(D) R --> T

Accepted Answer

Correct Answer: (A), (B), and (C)Concept -- Armstrong's Axioms and Closure Computation (from Ramakrishnan and Gehrke, Database Management Systems):Given FDs: P --> QR and RS --> T.(A) P --> R: TRUE. By the Decomposition rule from Armstrong's axioms: if P --> QR, then P --> Q and P --> R. So P --> R is directly derivable. TRUE.(B) PS --> T: TRUE. From P --> QR (so P --> R, thus PS --> RS by Augmentation with S). From RS --> T and PS --> RS: by Transitivity, PS --> T. TRUE.(C) PS --> Q: TRUE. From P --> QR: P --> Q (Decomposition). PS --> P (Decomposition of PS). By Transitivity: PS --> Q. Alternatively, P --> QR means P+ includes Q. So PS+ includes Q. PS --> Q. TRUE.(D) R --> T: FALSE. We cannot derive R --> T from the given FDs. The closure of R is {R} (R doesn't determine anything on its own with just the given FDs). R appears in RS --> T, but R alone doesn't determine T. Counterexample: R=1, S=1, T=0 with RS=11 triggering the FD -- but R=1 alone need not determine T. R --> T cannot be inferred.

Functional dependencies on relation U(P,Q,R,S,T): P --> QR and RS --> T. Which of the following FDs can be inferred?(A) P --> R(B) PS --> T(C) PS --> Q(D) R --> T

Master GATE-CS with Our Test Series

More Questions from Normal Forms (1NF, 2NF, 3NF, BCNF)

Frequently Asked Questions

Functional dependencies on relation U(P,Q,R,S,T): P --> QR and RS --> T. Which of the following FDs can be inferred?(A) P --> R(B) PS --> T(C) PS --> Q(D) R --> T

Master GATE-CS with Our Test Series

More Questions from Normal Forms (1NF, 2NF, 3NF, BCNF)

Frequently Asked Questions