Directions: When you normalize a database, you may answer in the form of dependency diagrams or

textual lists of attributes, but you must show the entire database $($including old tables, not just new tables$),$ and you must identify the primary key of each table. $($underlining all prime attributes is sufficient.$)$

$(10$pts$)$ Suppose there is a table $x$ with attributes $(A_{,}{B}_{,}C,D,E,F,G).$ Suppose that $AC,D,E$; that

$DE$; and that $FB.$

a$.(2$pts$)$ Identify all partial, transitive, and backwards dependencies.

b$.(2$pts$)$ Normalize to $2$NF$.$ Call the new table Y$.$

c$.(2$pts$)$ Normalize to $3$NF$.$ Call the new table Z$.$

d$.(2$pts$)$ Normalize to Boyce$-$Codd Normal Form $($BCNF$).$ Call the new table W$.$

e$.(2$pts$)$ Identify all foreign keys in the fully$-$normalized database. Indicate the name of the FK$,$ the table that contains the FK$,$ and the table the FK refers to$.$