## Definition A ==Venn Diagram== is a graphical representation of sets using overlapping circles (or other closed curves) drawn inside a rectangle that represents the universal set. The spatial overlaps visually encode intersections, unions, and complements, making it easier to reason about relationships among events. > [!example]- In a survey of 100 students, 60 like math, 50 like science, and 30 like both. How would a Venn Diagram help find how many like neither? > Draw two overlapping circles inside a rectangle (the universal set of 100 students). Place 30 in the overlap (both). Then math-only is $60 - 30 = 30$, science-only is $50 - 30 = 20$. The total who like at least one is $30 + 30 + 20 = 80$, so the number who like neither is $100 - 80 = 20$.