# RDBMS Questions and Answers – Functional-Dependency Theory

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This set of RDBMS Multiple Choice Questions & Answers (MCQs) focuses on “Functional Dependency Theory”.

1. A functional dependency f on R is _______ by a set of functional dependencies F on r if every instance of r(R) that satisfies f also satisfies F.
a) Logically Defined
b) Logically Derived
c) Logically implied
d) None of the mentioned

Explanation: Given a set F of functional dependencies on a schema, we can prove that certain other functional dependencies also hold on that schema. We say such FDs are logically implied by F. A functional dependency f on R is logically implied by a set of functional dependencies F on r if every instance of r(R) that satisfies F also satisfies f.

2. If F is a set of functional dependencies, then the closure of F is denoted by?
a) F*
b) Fo
c) F+
d) F

Explanation: If F is a set of functional dependencies, then the closure of F is denoted by F+. It is the set of all functional dependencies logically implied by F.

3. If a functional dependency is reflexive, B is a subset of A and A is the set of attributes, then
a) B→A holds
b) A→B holds
c) AB→C holds
d) None of the mentioned

Explanation: If a functional dependency is reflexive, B is a subset of A and A is the set of attributes, then A→B holds. This is called the reflexivity rule of Armstrong’s axioms.
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4. State true or false: Armstrong’s axioms allow us to generate all F+ for any given F
a) True
b) False

Explanation: Armstrong’s axioms allow us to generate all F+ for any given F and hence are called complete.

5. Armstrong axioms are called sound because?
a) They are expensive
b) They cannot generate correct functional dependencies
c) They allow us to generate the complete closure
d) They cannot generate incorrect functional dependencies

Explanation: Armstrong’s axioms are called as sound axioms because they do not generate incorrect functional dependencies.

6. State true or false: Functional dependencies are transitive
a) True
b) False

Explanation: All functional dependencies are transitive. This is the transitivity rule of Armstrong’s axioms.

7. If A→B, A→ C then which of the following is true?
a) A→BC
b) A→B
c) A→C
d) All of the mentioned

Explanation: Applying the union rule to the given question, we get, A→BC is true. The other two options are specified in the question itself.

8. If B is an attribute and A→B, Then B is said to be ________ by a.
a) Logically implied
b) Functionally implied
c) Logically determined
d) Functionally determined

Explanation: If B is an attribute and A→B, Then B is said to be functionally determined by a.

9. We say that a decomposition having the property F’+ = F+ is a __________ decomposition.
a) Dependency losing
b) Dependency preserving
c) Lossless
d) None of the mentioned

Explanation: We say that a decomposition having the property F’+ = F+ is a dependency preserving decomposition.

10. A _________ Fc for F is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F.
a) Canonical cover
b) Complete cover
c) Canonical dependency
d) Canonical clause

Explanation: A Canonical cover Fc for F is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F. In Fc, no functional dependency should contain an extraneous attribute and each left side of functional dependency should be unique.

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