Questions and Answers
Which of the following decompositions is considered nonadditive join decomposition?
A relation is in BCNF if it is in 3NF.
False
What is a multivalued dependency (MVD)?
An MVD X→→Y specifies that if two tuples share the same values for X, then they must also share two tuples with Y values corresponding to them.
An MVD that satisfies either (a) Y is a subset of X or (b) X ∪ Y = R is called a __________ MVD.
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Match the following types of normal forms with their definitions:
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Which of the following statements about functional dependencies is true?
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An MVD is called nontrivial if it satisfies conditions (a) or (b).
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What is the condition for two schemas R1 and R2 to form a nonadditive join decomposition with respect to a set F of functional dependencies?
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If two tuples t1 and t2 exist in a relation r such that t1[X] = t2[X], then it implies the existence of tuples t3 and t4 with t3[Y] = __________.
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In the context of multivalued dependencies, which of the following scenarios exemplifies a trivial MVD?
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Study Notes
Functional Dependency
- A functional dependency (FD) X → Y indicates that the values of Y are determined solely by the values of X.
- It reflects the semantics of the attributes within a relational database.
- Database designers utilize their understanding of attributes to define FDs in relations.
Example of Functional Dependencies in EMP_PROJ
- Ssn → Ename: An employee's Social Security Number uniquely determines their name.
- Pnumber → {Pname, Plocation}: A project's number uniquely identifies its name and location.
- {Ssn, Pnumber} → Hours: The combination of an employee's Ssn and project number uniquely determines their work hours on that project per week.
Types of Functional Dependencies
- Full Functional Dependency: Removal of an attribute from X means the dependency no longer holds. Example: {Ssn, Pnumber} → Hours.
- Partial Functional Dependency: The dependency still holds even after removing an attribute from X. Example: Ssn → Ename holds true even if Ssn is alone.
- Transitive Dependency: Exists if X → Z and Z → Y, indicating a chain of dependencies.
Join Dependencies and Fifth Normal Form (5NF)
- A relation schema R can be decomposed into R1 and R2 without losing information if the natural join of R1 and R2 results in R.
- Lossless decomposition becomes a concern when the number of decompositions is two; decomposing into more than two relations generally yields lossless decomposition.
- A join dependency (JD) JD(R1, R2,..., Rn) asserts that every legal state of R must support a nonadditive join decomposition into these relations.
Trivial Join Dependencies
- A join dependency is trivial if one of the schemas in JD equals R, which does not impose additional constraints.
Fifth Normal Form (5NF) Definition
- A relation is in 5NF if all nontrivial JDs imply that every Ri is a superkey of R, ensuring specific constraints on decompositions.
Example Situation: SUPPLY Relation
- A relation may be in 4NF but not in 5NF if it contains a join dependency JD(R1, R2, R3).
- Candidate keys and dependencies illustrate normalization levels; for instance, {Student, Course} as a candidate key indicates the relation is in 3NF but not BCNF.
Decompositions of Relations
- Possible decompositions from a given relation include pairs like {Student, Instructor} and {Student, Course}.
- All decompositions may lead to loss of functional dependencies, but a desirable decomposition avoids this by ensuring nonadditive join properties.
Multivalued Dependency (MVD) and Fourth Normal Form (4NF)
- An MVD X →→ Y specifies that if two tuples share X values, corresponding tuples with Y values must also exist.
- A trivial MVD occurs if Y is a subset of X or if X ∪ Y equals R; otherwise, it is nontrivial.
- Example: In relation EMP_PROJECTS, Ename →→ Pname is a trivial MVD because Pname is dependent on Ename.
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Description
Test your understanding of functional dependencies in relational databases with this quiz. Explore concepts such as full and partial dependencies using practical examples. Challenge yourself to identify how attributes influence database design and integrity.
