GATE CS 2024 Set 1 — Question 44
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0EasyFunctional DependenciesNormalizationDatabasesArmstrong's Axioms
Databases → Normalization → Armstrong's Axioms
Last updated
Question
The symbol indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?
Correct answer
(B) (X, Y) arrow (Z, W) implies (X, Y) arrow Z; (C) ((X, Y) arrow Z and W arrow Y) implies (X, W) arrow Z; (D) (X arrow Y and Y arrow Z) implies X arrow Z
Solution
We evaluate each option based on Armstrong's Axioms and derived rules for functional dependencies:(A) implies
This is FALSE. We cannot simply remove attributes from the determinant (left side) of a functional dependency. For example, if is StudentName and is CourseID, together they might determine Grade (), but StudentName alone does not determine Grade.(B) implies
This is TRUE by the Decomposition Rule. If a set of attributes determines a set of attributes, it determines any subset of those attributes.(C) implies
This is TRUE by the Pseudotransitivity Rule.
Proof:
This is TRUE by the Transitivity Rule (one of Armstrong's Axioms).Therefore, options (B), (C), and (D) are correct.
This is FALSE. We cannot simply remove attributes from the determinant (left side) of a functional dependency. For example, if is StudentName and is CourseID, together they might determine Grade (), but StudentName alone does not determine Grade.(B) implies
This is TRUE by the Decomposition Rule. If a set of attributes determines a set of attributes, it determines any subset of those attributes.(C) implies
This is TRUE by the Pseudotransitivity Rule.
Proof:
1.
W → Y (Given)2.
XW → XY (Augmentation of 1 with )3.
XY → Z (Given)4.
(D) implies XW → Z (Transitivity on 2 and 3)X → ZThis is TRUE by the Transitivity Rule (one of Armstrong's Axioms).Therefore, options (B), (C), and (D) are correct.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Normalization
2026 Set 2 Q15In the context of DBMS, consider the two sets T and S given below. | T | S | |---|---| | I:…2026 Set 2 Q20Consider concurrent execution of two transactions and in a DBMS, both of which access a…2026 Set 1 Q30Let and be the attributes of a relation in a relational schema. Let…2026 Set 1 Q31In the context of relational database normalization, which of the following statements is/are true?2026 Set 2 Q42In the context of schema normalization in relational DBMS, consider a set F of functional…