Visualizing Operations on Two Sets (Intersection, Difference, Complement)

This GeoGebra example demonstrates how standard set operations on two sets can be represented visually in the plane and then used to solve short checking problems. It focuses on the geometric/analytical interpretation of set theory: intersection (common part), union (combined coverage), set difference (A\B and B\A), and complement/relative complement as the “remaining” region after removing parts. The construction uses geometry to make the algebraic operations tangible. From the construction summary: Point, Segment, and Polygon define key points, edges, and bounded regions; Vector supports auxiliary directed constructions; Intersect computes boundary intersection points; Arc and multiple arc objects (e.g., arcARight/arcALeft and arcBRight/arcBLeft) build curved boundaries; Locus generates loci to form evolving outlines. Objects such as INTUP/INTDWN represent intersection boundaries, while named difference objects like AMinusB and BMinusA correspond directly to the displayed “set minus” results. ddMenu and testo5–testo9 help switch between operations and verify understanding. Suitable for upper secondary and introductory university learners studying set theory and for classroom visualization with GeoGebra.