Venn diagram

Definition

A Venn diagram is a visual tool used to illustrate the relationships and interactions between different sets. It typically consists of overlapping circles, each representing a set, with the overlap showing elements common to multiple sets.

5 Must Know Facts For Your Next Test

1. Venn diagrams are used to solve problems involving unions, intersections, and complements of sets.
2. The union of two sets A and B in a Venn diagram is represented by all the areas covered by either circle A or circle B.
3. The intersection of two sets A and B is depicted by the overlapping area of circles A and B.
4. Elements not in any set are shown outside the circles but within the universal set boundary.
5. Venn diagrams can be extended beyond two sets to three or more, though they become increasingly complex.

Review Questions

• What does the intersection of two sets represent in a Venn diagram?
• How would you depict the union of three sets using a Venn diagram?
• What is the significance of the shaded regions in a Venn diagram?

Related terms

Set:

A collection of distinct elements or objects considered as an entity.

Union:

The set containing all elements from both sets being considered, denoted as $A \cup B$.

Intersection:

The set containing only the elements common to both sets being considered, denoted as $A \cap B$.