Consider the following two relations R1(ABCDE) with functional d
Consider the following two relations
R1(ABCDE) with functional dependencies {AB → CDE}, AC → BDE, B → C, C → B, C → D, B → E}
R2(ABCD = {AB → C, AB → D, C → B}
The highest normal form of relations R1 and R2 respectively are:A. 1NF, 2NF
B. 2NF, 3NF
C. 1NF, 3NF
D. 2NF, 1NF
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
First normal form (1 NF): a relation is in 1NF, if domain of each attribute contains only atomic values.
2NF: If there is no partial dependency in the functional dependency, then that FD is in 2NF.
3NF: A relation is in 3NF if it is in 2NF and not contain transitive dependency. If A -> B is a functional dependency, then either B must be key attribute or A is the key.
BCNF: for this relation should be in 3NF, and if functional dependency A- > B exist, then A must be the key for a relation to be in BCNF.
Explanation:
CASE 1: Given relation R1 as:
AB → CDE // BCNF, as AB is the key
AC → BDE, // BCNF, as AC is the key
B → C // 3NF, as C is the prime attribute
C → B, // 3NF, as B is the prime attribute
C → D // 1NF, not in 2NF as partial dependency exist
B → E // 1NF, not in 2NF as partial dependency exist.
Key for this relation is AB, AC.
So, highest normal for relation R1 is 1NF.
CASE 2: Relation R2 is given as :
AB → C, // BCNF, as AB is the key
AB → D // BCNF, as AB is the key
C → B // 3NF, as B is the prime attribute
Key for this relation is AB.
The highest normal form for relation R2 is 3NF.