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
Answer
Answer: c [Reason:] 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
Answer
Answer: c [Reason:] 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
Answer
Answer: b [Reason:] 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.
4. State true or false: Armstrong’s axioms allow us to generate all F+ for any given F
a) True
b) False
Answer
Answer: a [Reason:] 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
Answer
Answer: d [Reason:] 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
Answer
Answer: a [Reason:] 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
Answer
Answer: d [Reason:] 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
Answer
Answer: d [Reason:] 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
Answer
Answer: b [Reason:] 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
Answer
Answer: a [Reason:] 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.
