Venn Diagrams

Venn diagrams are a tool used in set theory to visually display and analyse relationships between different sets.
A Set is typically represented in a Venn Diagram by a circle. Each circle encapsulates the elements that belong to a particular set.
The Universal Set, represented by a rectangle, contains all possible elements in the context of the problem.
Intersection of sets (common elements between sets) is visually represented by the overlap of circles.
Unique elements within sets are displayed in non-overlapping portions of each circle.
Union of sets is visually represented by the total area covered by the circles of those sets - all elements that belong to either set or both.
Empty set or Null set is a set with no elements. It is represented by a circle within the universal set but outside all other sets.
Complement of a set is visually depicted as all elements in the universal set that are not part of the given set. This is shown by the area of the rectangle (universal set) that is not covered by the circle representing the set.
Disjoint sets have no common elements and are displayed as non-overlapping circles.
To represent the intersection of more than two sets, the circles corresponding to these sets overlap each other at a common point.
For problems involving conditional probability and independence, Venn Diagrams are extremely useful tools.

Remember that a clear, accurate Venn diagram often makes calculation and problem-solving easier and less prone to error. Always label your sets clearly and double-check your diagram against the problem or question description.