$1)$ You are given table T$($A$,$B$,$C$,$D$).$ The primary key is the concatenation of A and B$.$ The table is in $2$NF but not in $3$NF$.$

State whether these statements are true or false and explain why?

C $->$ D$$ b$)$ A $->$C c$)$ A $->$D d$)$ A $->$ B e$)$ C $->$ A

$2)$ Given table T$($A$,$B$,$C$,$D$,$E$,$F$)$ A$,$B $->$ C $$ C$->$D$$ A$->$E$$ B$->$F

What is the correct decomposition into $3$NF$?$ Indicate the primary key for each table.

$3)$ Given table T$($A$,$B$,$C$,$D$)$ in which A $->$ B$,$ A $->$ C$,$ A $->$ D$,$ B $->$ C and C $->$ D

What is the correct decomposition into $3$NF$.$ Indicate the primary keys.