This Demonstration illustrates some fundamental set operations when applied to geometric regions in a plane (similar to a Venn diagram). The operations include union ⋃, intersection ⋂, set difference \, and symmetric difference Δ (analogous to XOR).
You can resize the two regions, an ellipse and a polygon, with the controls and drag the polygon using the Locator at its center.
The result of the chosen operation is the green region with the red border. Its surface area and centroid are continuously updated below the graphics.