Consider following relation with schema R$($A$,$B$,$C$,$D$)$ and functional dependencies:

$1.$ ABC, CD$,$ and DA$.$

$2.$ BC$,$ and BD$.$

$3.$ ABC, DC$,$ and B$-$D$.$

a$.$ List all candidate keys

b$.$ Check whether the relation is in $3$NF or not.

c$.$ Decompose the relations, as necessary into collections of relations that are in $3$NF$.$

d$.$ Decompose the relations, as necessary into collections of relations that are in BCNF$.$