Set Theory/Examples

Equations $A \cup \paren {X \cap B} = C$, $\paren {A \cup X} \cap B = D$
=== Simplify $\paren {A \cap B} \cup \paren {C \cap A} \cup \relcomp {\Bbb U} {\relcomp {\Bbb U} A \cup \relcomp {\Bbb U} B}$ ===

Let $A$, $B$ and $C$ be sets defined by circles embedded in the complex plane as follows: