Lesson 3

Lesson 3: Applications of Sets

 

Focus

 

In small schools, many students play on multiple sports teams. Scheduling games can be challenging since many players are on multiple teams.

 

Consider the following example.

 

In a small Alberta school, there are 14 Grade 12 students. Of these students, 6 play volleyball and 7 play basketball. There are 3 students who do not play either sport.1 The total number of students adds up to 16, but how is this possible if there is a total of only 14 Grade 12 students?

 

Set notation can help solve problems similar to this one by determining how many players play each sport, how many players play both sports, and how many students don’t play either sport. From that information, schedules can be made that don’t overlap and thus avoid forcing any student on more than one sports team to miss any games.

 

How would you solve this problem?

 

Lesson Outcomes

 

At the end of this lesson, you will be able to

• describe how to use the principle of inclusion and exclusion when solving problems involving the union of sets
• solve problems involving unions and intersections of sets

Lesson Questions

 

In this lesson you will investigate the following questions:

• What do the words and, or, and not represent in set theory questions?
• How can set theory be used to solve problems?

Assessment

 

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 3 Assignment (Download the Lesson 3 Assignment and save it in your course folder now.)

• course folder submissions from Try This and Share activities

• additions to Glossary Terms and Formula Sheet
• work under Project Connection

1 Adapted from PRINCIPLES OF MATHEMATICS 12 by Canavan-McGrath et al. Copyright Nelson Education Ltd. Reprinted with permission.