An organization needs to maintain database having five attributes $A,B,C,D,E$. These attributes are functionally dependent on each other for which functional dependency set $F$ is given as:

$F={A\rightarrow BC,\ D\rightarrow E,\ BC\rightarrow D,\ A\rightarrow D}$

Consider a universal relation $R(A,B,C,D,E)$ with functional dependency set $F$. Also all attributes are simple and take atomic values only.

Assume that given table $R$ is decomposed in two tables:

$R_1(A,B,C)$ with functional dependency set

$f_1={A\rightarrow B,\ A\rightarrow C}$

and

$R_2(A,D,E)$ with FD set

$F_2={A\rightarrow D,\ D\rightarrow E}$

Which of the following option is true w.r.t. given decomposition?