Venn Diagrams Basics

Venn Diagrams are diagrams with overlapping circles that indicate how much different groups have in common.
They are typically used to depict the similarities and differences between different sets or groups.
Circles on a Venn Diagram represent events or classes of events in a universal set. The universal set is typically represented by a rectangle.

Drawing Venn Diagrams

Identify the universal set, which contains all the possible elements or outcomes.
Each set within the universal set is represented by a circle. Name each circle according to the set it represents.
Fill in the overlapping areas first. These represent elements common to the sets your circles represent.
Fill in the non-overlapping areas. These represent elements unique to each set.

Venn Diagrams can be used to calculate probabilities. The entire rectangle represents the sample space (i.e., all possible outcomes), and the circles represent events.
The probability that an event happens can be found by comparing the size (e.g., area) of the event (i.e., circle or part of a circle) to the size of the sample space (i.e., the rectangle).

Venn Diagrams help visualise the relationships between different sets and subsets. They can be used to identify the intersection (common elements) and union (all elements) of sets.
A union of sets includes all elements that are in either set, or both sets, often represented by the symbol ‘∪’. On a Venn diagram, it’s the combination of the areas of the sets involved.
An intersection of sets is where two (or more) sets overlap, containing the elements that are common to all sets involved. It’s represented by the symbol ‘∩’. On a Venn diagram, it’s the overlapping area of the sets.

Remember:

A point inside a circle but outside another represents an element that is in the first set but not in the second.
A point outside all circles represents an element that is not in any of the sets.
A point in the intersection of two circles represents an element that is in both sets.