51.  Let r be a relation instance with schema R = (A, B, C, D). We define r1 = ΠA, B, C (r) and r2 = ΠA.D (r). Let s = r1 * r2 where * denotes natural join. Given that the decomposition of r into r1 and r2 is lossy, which one of the following is TRUE? 
Discuss 
Answer: (c).r ⊂ s

52.  Consider a relation scheme R = (A, B, C, D, E, H) on which the following functional dependencies hold: {A–>B, BC–>D, E–>C, D–>A}. What are the candidate keys of R? 
Discuss 
Answer: (d).AEH, BEH, DEH

53.  The relation scheme Student Performance (name, courseNo, rollNo, grade) has the following functional dependencies: name, courseNo → grade rollNo, courseNo → grade name → rollNo rollNo → name The highest normal form of this relation scheme is 
Discuss 
Answer: (b).3 NF

54.  Consider the following functional dependencies in a database: Data_of_Birth → Age Age → Eligibility Name → Roll_number Roll_number → Name Course_number → Course_name Course_number → Instructor (Roll_number, Course_number) → Grade The relation (Roll_number, Name, Date_of_birth, Age) is: 
Discuss 
Answer: (d).None of the above

55.  Relation R with an associated set of functional dependencies, F is decomposed into BCNF. The redundancy (arising out of functional dependencies) in the resulting set relations is. 
Discuss 
Answer: (a).Zero

56.  With regard to the expressive power of the formal relational query languages, which of the following statements is true? 
Discuss 
Answer: (c).Relational algebra has the same power as safe relational calculus

57.  Relation R is decomposed using a set of functional dependencies, F and relation S is decomposed using another set of functional dependencies G. One decomposition is definitely BCNF, the other is definitely 3NF, but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of F and G are available). 
Discuss 
Answer: (c).BCNF definition

58.  From the following instance of a relation scheme R (A, B, C), we can conclude that : A B C 1 1 1 1 1 0 2 3 2 2 3 2 
Discuss 
Answer: (c).B does not functionally determine C

59.  Consider a schema R(A,B,C,D) and functional dependencies A>B and C>D. Then the decomposition of R into R1(AB) and R2(CD) is 
Discuss 
Answer: (c).dependency preserving but not lossless join

60.  Suppose the adjacency relation of vertices in a graph is represented in a table Adj(X,Y). Which of the following queries cannot be expressed by a relational algebra expression of constant length? 
Discuss 
Answer: (d).List all vertices reachable from a given vertex
