Task 1:
STUDENT(snumber, first-name, last-name, ccode) snumber → first-name, last-name
Therefore, first-name, last-name columns will have redundancies as a student enrolls in more classes.
HOTEL(name, city, capacity, enumber, salary) name, city → capacity enumber → salary
Therefore; capacity, salary will have redundancies.
WAREHOUSE(wname, address, part, quantity) address → wname wname → address wname, part → quantity Address, part → quantity
Therefore: address, wname, quantity will have redundancies so schema should be decomposed.
LIBRARY(cnumber, title, price, isbn) title → price, ISBN cnumber → title, price, ISBN ISBN → title, price
Therefore: title, price, ISBN will have redundancies so schema should be decomposed.
Task 2:
Q1: R(A, B, C, D, E) and {A → B, C → A} -Derivations that identify minimal keys:
C → B; transitive axiom
C → AB; union
Therefore minimal key identified.
-Minimal keys:
-CDE
Q2: R(A, B, C, D, E) and {A → E, E → C, CD → A} -Derivations that identify minimal keys:
A → C; transitive axiom
A → EC; union
ED → DC; augmentation axiom
ED → A; transitive axiom
ED → ADC; union
Therefore 3 minimal keys identified.
-Minimal keys:
-BED, BAD, BCD
Q3: R(A, B, C, D, E) and {D → A, DA → B, DE → ABC} -Derivations that identify minimal keys:
No derivations required.
Minimal key identified.
-Minimal keys:
-DE
