Given the following relation and functional dependencies, answer questions (a) –

Question

Given the following relation and functional dependencies, answer questions (a) – (d). Then answer question (e).
T (A, B, C, D, E, F, G)
A,B --> C, D, E, F, G
C,D --> A, B, E, F, G
E --> D
C --> F
B --> G

(a) Show that the relation T above is only in 1NF and does not conform to any higher normal forms. Given that the primary key is (A, B), determine any alternate keys.

(b) Normalize the relation T up to 2NF relations only. Indicate the primary key of each relation.

(c) Further normalize the result of (b) above up to 3NF only. Indicate the primary key of each relation.

(d) Further normalize the result of (c) above up to BCNF only. Indicate the primary key of each relation

(e) State two further problems that can occur in BCNF relations requiring further normalization beyond BCNF.

Explanation / Answer

Dear,

a. a Relation R is in 1NF, allow relations with in relations

 Alternate keys are C, D, E

b. A relation schema R is in 2NF if every nonprime attribute of A in R is fully functionally dependent on primary key of R

 AB--> from B --> G
CD--> F from C --> F

Primary keys are B and C
Full functional dependency need to satisfies

c.

A relation R is in third normal form if, when ever a nontrival funcitonal dependency X-->A hols in T,

X is a superkey of R

A is a prime attribute of R

Need to satisfy transitive dependency
AB-->C
C -->F
AB-->F

AB-->E
E-->D
AB-->D

CD-->G

d. A relation R is in BCNF whether non-trival functional dependency X-->A holds in R, then X is a super key of R

Here super key is: A and D

C --> F
B --> G

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