Primary Key: $\{$Dcode$,$ Dcollege$\}$ Unique Keys: $\{$Dname$,$ Dcollege$\}$

FDs:

Dcode $->\{$Dname$,$ Doffice, Dphone$\}$

Dname $->\{$Dcode$,$ Doffice, Dphone$\}$

Courses Relation

Primary Key: $\{$Cnum$,$ Cdept$\}$ Unique Keys: $\{$Cname$,$ Cdept$\}$

FDs:

Cnum $->\{$Cname$,$ Cdesc, Credit, Level$\}$

Cname $->\{$Cnum$,$ Cdesc, Credit, Level$\}$

Sections Relation

Primary Key: $\{$Sec course, Sec num, Semester, Year$\}$

Grade Relation

Primary Key: $\{$Snum$,$ Sec course, Sec num, Semester, Year$\}$

$2.$ For each decomposition step, state the reasons behind the decomposition.

$3.$ Your answer should include the following for each relation:

$$ Initial form $($e$.$g$.,1$NF$)$ with an explanation based on the given functional

dependencies.

$$ Decomposition step to the next normal form $($e$.$g$.,2$NF$)$ with reasons.

$$ Continue this process up to $4$NF$.$