section_path: Euler and Venn diagrams
section_name: Euler and Venn diagrams
paragraph_text: Euler and Venn diagrams
  
  An Euler diagram is a graphical representation of a collection of sets; each set is depicted as a planar region enclosed by a loop, with its elements inside. If A is a subset of B, then the region representing A is completely inside the region representing B. If two sets have no elements in common, the regions do not overlap.
  
  A Venn diagram, in contrast, is a graphical representation of n sets in which the n loops divide the plane into 2 zones such that for each way of selecting some of the n sets (possibly all or none), there is a zone for the elements that belong to all the selected sets and none of the others. For example, if the sets are A, B, and C, there should be a zone for the elements that are inside A and C and outside B (even if such elements do not exist).