Set Theory/Examples/A cup (X cap B) = C, (A cup X) cap B = D

Example in Set Theory
Let $A, B, C, D$ be subsets of a set $S$.

Let there exist $X \subseteq S$ such that:
 * $A \cup \paren {X \cap B} = C$
 * $\paren {A \cup X} \cap B = D$

Then:
 * $A \cap B \subseteq D \subseteq B$

and:
 * $A \cup D = C$

Proof
Then: