# Set Theory/Examples/Union of Intersections with Set Complements/3 Circles in Complex Plane

## Example in Set Theory

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

 $\displaystyle A$ $=$ $\displaystyle \set {z \in \C: \cmod {z + i} < 3}$ $\displaystyle B$ $=$ $\displaystyle \set {z \in \C: \cmod z < 5}$ $\displaystyle C$ $=$ $\displaystyle \set {z \in \C: \cmod {z + 1} < 4}$

$\paren {A \cap \tilde B} \cup \paren {B \cap \tilde C} \cup \paren {C \cap \tilde A}$, where $\tilde A$ denotes the complement of $A$, can be illustrated graphically as:

where the union of the intersections is depicted in yellow.