Union, Intersection, and Difference of Two Sets via Circles

This example visualizes how two sets combine by showing the geometric regions formed by two overlapping circles. It demonstrates the set operations Union (U), Intersection (∩), and Difference (\) as clearly distinguishable areas on the plane. The key math ideas are elementary set theory—how overlapping domains correspond to intersection and how combining or subtracting domains changes the resulting region—often linked to geometric intuition about area and decomposition. In GeoGebra, it is constructed using commands Sample, Union, Intersection, Circle, Intersect, and CircleArc: two circles are created (Circle), their intersection points are found (Intersect), the overlapping regions are computed (Intersection), the combined coverage is built (Union), and arc/region components are additionally handled via CircleArc. Labeled and auxiliary objects (e.g., points/lines like A, B, l1, l2, and result regions/labels such as text1–text12 with interactive elements like button1) support clear visualization and interaction. Suitable for middle/high school and early university instruction on set theory, geometric construction, and mathematical visualization.