Venn Diagrams

• Venn diagrams are a diagrammatic representation of sets and the relationship between them.
• A circle in a Venn diagram represents a set.
• The universal set – which contains all possible elements – is usually represented by a rectangle enclosing the circles.
• An element that belongs to a particular set is represented by a point inside the corresponding circle.
• An element that does not belong to a specific set is placed outside the circle but within the rectangle.
• The region where two sets overlap denotes the intersection of those sets. The intersection represents elements common to both sets.
• The union of two sets is represented by the total area covered by the two circles. The union includes all elements that belong to either or both sets.
• To represent the complement of a set – which includes all elements not in a certain set but located in the universal set – shade the area outside the specific set but within the rectangle.
• Venn diagrams are used in solving problems involving union, intersection, difference and compliment of sets.
• When determining the difference between two sets (A - B), you are finding all the elements that belong to set A but not set B.
• Venn diagrams are also used in solving problems involving conditional probability, which is the chance of an event occurring given that another event has already occurred.