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.
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Point Sets: $123 \ \text{(d)}$