5.1 Organized Counting with Venn Diagrams

1. 5.1 Organized Counting with Venn Diagrams

2. Venn Diagram

3. Venn Diagram • Groups things based on if things are in common or not in common. • Each group is called a Set. • The set of all possible things is called the universal set, S

4. Elements and Sets

5. Example • There are 10 students on the volleyball team and 15 on the basketball team. When planning a field trip with both teams, the coach has to arrange transportation for a total of only 19 students. • Use venn diagram to illistrate this situation • Why can’t I just add each of the teams? • How many students in total are there between both teams?

6. Principle of Exclusion • If you are counting the total number of elements in two sets that have common elements, you must subtract the common elements so they are not counted twice!

7. Principle of Exclusion

8. Union and Intersection • The union of two sets, denoted , means all the elements in set A and in set B • The intersection of two sets, denoted , means the elements that are both A and B

9. Example • A drama club is putting on two one-act plays. There are 11 actors in the Feydeau farce and 7 in the Moliere piece. • If 3 actors are in both plays, how mnay actors are there in total? • Use a venn diagrams to calculate how many students are in only one of the two plays

10. 3 Sets • Of the 140 grade 12 students in a High School, 52 have signed up for biology, 71 for chemistry, and 40 for physics. The science students include 15 who are taking bio and chem, 8 who are taking chem and phys, 11 who are taking bio and phys, and 2 who are taking all three. • How many students are not taking any of the courses? • Illustrate using venn

11. Assignment • Pg 270 #’s 1-7