Set Theory/Examples/Intersection of Unions/3 Circles in Complex Plane

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Example in Set Theory

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

\(\ds A\) \(=\) \(\ds \set {z \in \C: \cmod {z + i} < 3}\)
\(\ds B\) \(=\) \(\ds \set {z \in \C: \cmod z < 5}\)
\(\ds C\) \(=\) \(\ds \set {z \in \C: \cmod {z + 1} < 4}\)

$\paren {A \cup B} \cap \paren {B \cup C}$ can be illustrated graphically as:


where the intersection of the unions is depicted in yellow.