That is, how to represent set $A$ in terms of D, B, C given the equation above? Or is it possible?
N.B. To represent a set is to define this set, i.e. $A = \cdots$, not $A \subseteq \cdots$.
That is, how to represent set $A$ in terms of D, B, C given the equation above? Or is it possible?
N.B. To represent a set is to define this set, i.e. $A = \cdots$, not $A \subseteq \cdots$.
If $D\cap C=\varnothing$ and $B\subseteq D\cup C$, the solutions are the sets $A$ such that $D\setminus B\subseteq A\subseteq D\cup C$. Otherwise, there is no solution.
To see this, picture $B$ as the upper half of a square, $C$ as its left half and $D$ as its right half. Then $A$ must contain the lower-right quarter and must not meet the top-left quarter.
Edit: There exists a unique solution $A$ if and only if $D\cap C=\varnothing$, $B\subseteq D\cup C$ (existence) and $D\setminus B=D\cup C$ (uniqueness). These conditions are equivalent to $B=C=\varnothing$, then the unique solution is $A=D$ (obviously).