Problem $3[20]$ For each of the following relation schemas and sets of FD$$s: a$)$ R $($A $,$B $,$C $,$D $)$ with FD$$s AB$$C$,$ C$$D and D$$A$.$ b$)$ R$($A$,$ B$,$ C$,$ D$)$ with FD$$s A B $$C $,$B C$$D$,$ CD $$ A$,$ and AD $$B$.$ do the following: i$)$ Indicate all the BCNF violations. Do not forget to consider FD$$s that are not in the given set, but follow from them. However, it is not necessary to give violations that have more than one attribute on the right side. ii$)$ Decompose the relations, as necessary, into collections of relations that are in BCNF$.$