Show me the steps to solve Apply the BCNF algorithm to this relation:

R$($A$,$ B$,$ C$)$ and the two functional dependencies below:

A $->$ B

BC $->$ A

Determine whether R is in BCNF$.$ If it is not, decompose R into relations that are in BCNF$.$

Which one of the following is the result?

Group of answer choices

R$1($A$,$ B$)$ and R$2($A$,$ C$)$

R$1($A$,$ C$)$ and R$2($B$,$ C$)$

R is already in BCNF

R$1($A$,$ B$)$ and R$2($B$,$ C$)$