Normalization in DBMS, solved exercises in DBMS, lossless join decomposition, dependency preserving decomposition, bcnf decomposition
RDBMS MCQ solved quiz and answers
1. Let us assume that a relation R (A, B, C, D, E) with set of functional dependencies F = {A → BC, C → D} is decomposed into relations R1 (A, B, C) and R2 (A, D, E). This decomposition is ___________.
a) Lossless join decomposition
b) Dependency preserving decomposition
c) Not a dependency preserving decomposition
d) Lossy decomposition
Answer: (a) and (c) Common attribute between R1 and R2 is A, and, attribute A determines all attributes of R1. Hence, it is a lossless decomposition. It is not a dependency preserving decomposition because the FD C → D is lost. Lossless join decomposition Decomposition of relation R into R1 and R2 is said to be lossless join decomposition if one of the following holds;
Dependency preserving decomposition If a relation R with set F of functional dependencies is decomposed into relations R_{1}, R_{2}, R_{3}, …, R_{i} then the closure of set of functional dependencies for these relations should satisfy the following;

2. Let us assume that a relation R (A, B, C, D, E, F, G, H) with set of functional dependencies F = {AB → E, C → D, D → E, FG → A} is decomposed into relations R1(ABE), R2(CD), R3(FGA) and R4(BCFGH). The decomposition _____.
a) is resulted in all BCNF relations
b) is dependency preserving decomposition
c) is not a dependency preserving decomposition
d) is lossless decomposition
Answer: (a) and (c) R1(ABE), R2(CD), R3(FGA) and R4(BCFGH). Keys are underlined. All relations are in BCNF. The functional dependency D → E is lost. Hence, decomposition of R into R1, R2, R3 and R4 is not a dependency preserving decomposition. 
3. Consider a relation R(A, B, C, D, E) with the set of functional dependencies F = {A → B, B → E, E → A}. Relation R is in ____.
a) Unnormalized form
b) Third Normal Form
c) BoyceCodd Normal Form
d) Domain Key Normal Form
Answer: (b) 3NF The candidate keys for R are ACD, BCD, and ECD. No nonkey dependencies found in R. Hence, relation R is in third normal form. 
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