Venn Diagrams

These activities will work with the Venn Diagram as a counting technique.

For each diagram below, shade the indicated region

Rides a bike only      Rides & roller blades







Rides, blades & skateboards Participates in exactly one activity









II. Sketch a Venn diagram to illustrate the given the facts about ...

a) a class of students

- In a class of 32 students, 25 are freshman.

- Ten of the freshman girls play sports.

- 12 girls play sports.

- Seven Freshman boys play sports.

- 21 students play sports.

- Five freshman girls do not participate in a sport.







How many girls are in the class?_____________

b) a group of 90 musicians.

- 12 musicians played in the marching band and played the trumpet.

- 18 musicians played the trumpet.

- 75 musicians were in the marching band.






How many musicians were neither in the marching band, nor played the trumpet?____

How many musicians were not in the marching band?_______

c) a club of varsity athletes

- 25 athletes played soccer

- 7 athletes played soccer and baseball

- 14 athletes played baseball

- 9 athletes played tennis

- 7 athletes played soccer and baseball

- 6 athletes played soccer and tennis

- 4 athletes played baseball and tennis

- 2 athletes played all three sports











How many athletes played soccer, but not baseball or tennis?__________

How many athletes plated soccer and baseball, but not tennis?_________

How many athletes played just one of the three sports?______________


The Discrete Mathematics Project