Question

Given the following schema

AB ⟶ CD
A ⟶ B
B ⟶ E
E ⟶ F
A ⟶ F
G ⟶ H
H ⟶ E
GC ⟶ H
G⟶E

Required:
a. Find a minimal cover of this schema.
b. Find a key of this schema.
c. Find a 3rd normal form decomposition of this schema.
d. Find a BCNF decomposition of this schema.

Answer 1

a)

A ⟶ BCD , B ⟶ E , E ⟶ F , G⟶ H , H ⟶ E

b) AG

c) attached below

d ) attached below

Step-by-step explanation:

a) Minimal cover of this schema

This can be written following the steps below

step 1 : AB ⟶ C, AB ⟶ D , A ⟶ B , B ⟶ E, E ⟶ F , A⟶F, G ⟶ H, H ⟶ E, GC⟶H, G ⟶ E

removing redundant FD

AB ⟶ C , AB ⟶ D , A ⟶ B, B ⟶ E, E ⟶ F, G ⟶H , H⟶ E ,

eliminating p if Q⁺ contains p

Finally the Minimal cover of the schema

A ⟶ BCD , B ⟶ E , E ⟶ F , G⟶ H , H ⟶ E

B) Key of this schema

AG is the key of this schema given that ( AG )⁺ = ABCDEFGH

C) Determine the 3rd normal form decomposition

attached below

D) BCNF decomposition

attached below