Q$2.(25$ pts$.)$ Consider a relation $R(A,B,C,D,B,F,G)$ with the following functional dependencies:

$\{AB,CAD,CEB,EFC\}$

Compute the Boyce$-$Codd Normal Form $($BCNF$)$ decomposition of R$.$ Indicate each step you make in your computation, by showing the relation to which you apply the step and the violation of BCNF that you use during that decomposition step. Indicate clearly your end result: the relations, their attributes, and their keys.