Discrete Mathematics Project

Counting Techniques Activity


Venn Diagrams (John Long)


(1) Students will be able to use Venn Diagrams to represent a variety of information

(2) Students will use the Venn Diagrams to answer questions.


This activity presents a variety of problems for the students to investigate the power of Venn Diagrams. This activity is envisioned to be used prior to a probability unit to introduce a counting technique when the elements are not mutually exclusive.

Problem Statement

Discuss the difference between disjoint events and events that are not mutually exclusive. Use a simple example in your class to describe the differences. (E.g. The group of boys and the group of girls in the class. Then the group of band members and the group of math students.) Use a Venn Diagram to describe the situation. The Venn Diagram will be used in later work when finding the probability of events that are not disjoint.

Instructor Suggestions

(1) Set the stage be discussing the "Problem Statement.

(2) Distribute the activity sheet.

(3) Allow the students, in groups of two, to work on the activity.

(4) On an overhead have each group present one of their Venn Diagram. More than one group will present each diagram which should allow for discussion on their differences.


Venn Diagram activity sheet

Overhead sheets and pens


Introduction(10 min.), Working in groups of 2 (20 min.), Diagram Presentations and discussion (15 min.)

Mathematics Concepts

Discrete Mathematics Concepts

Counting Techniques, Mutually exclusive sets, Multiplication and Addition principals, Probability.

Related Mathematics Concepts

Venn Diagrams

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Geometry, Discrete Mathematics

Colorado Model Content Standards Addressed

Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity could be integrated into any level of mathematics. The purpose of the activity could be simply to introduce Venn Diagrams to the students. This activity could also be used to introduce non-disjoint sets and finding the probability of non-disjoint sets.

Further Investigation

Students could research the mathematician who developed the Venn diagram. Using the same activity, you could find various probabilities. (e.g. From Part III, if a player was picked at random, what is the probability that he/she played only soccer?)



Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W.G. Greeman and Company.

Joanie Carew. Broomfield High School. #1 Eagle Way. Broomfield, CO. 80020

Last updated January 16, 1997