This is a subjective question, hence you have to write your answer in the Text$-$Field given below.

Assume that the relational $R$ with schema $R(A,B,C,D,E,F),$ with the following set $(F)$ of

functional dependencies. $F=\{ABC$;$CD$;$DEF\}.$ If $R$ is decomposed into three relations$-$

$R1(A,B,E),R2(A,B,C,F),R3(A,B,D),$ do the following.

$($a$)$ Check if the above decomposition is lossless or not.

Use matrix approach discussed in the lectures$/$textbook$.$ You are required to give the

initial matrix, mention the possible modifications to the matrix, and give the final

answer$).$

$[3$Marks$]$

$($b$)$ Give the projection of $F$ on $R1,R2$ and $R3($i$.$e$.,{}_{R1}(F),{}_{R2}(F)$ and $\{$:${}_{R3}(F)).$

$[2$ Marks$]$