Concept guide
Area: intersection and union of half-open rectangles, recounted by unit cells
In an equal-unit orthonormal frame let A=[0,4)×[0,3) and B=[2,6)×[1,5). Find the areas of A and B, find the intersection A∩B and its area, find the area of A∪B by inclusion and exclusion, and recount it independently as the number of distinct unit cells. Then let C=[4,7)×[0,3) (touching A only at x=4) and Z=[3,3)×[0,5) (zero width), and find the areas of A∩C, A∪C and Z.