Consider a relation R$($A$,$B$,$C$,$D$)$ and the functional dependencies that hold over R:

ABC$->$D D$->$A

$1-$ Consider the decomposition of R into R$1($A$,$B$,$C$)$ and R$2($B$,$C$,$D$).$ Could this

decomposition have been the result of applying the BCNF decomposition algorithm to

R$?$

$2-$ Is R$1$ and R$2$ a lossless decomposition?