1. SPCR.1a – Lesson A Levels 1 – 3 Describe events as subsets of a sample space and use Venn diagrams to represent intersections, unions, and complements. Introduction to Venn Diagrams
D. Otap – Fall 2016

2. Sets
Definitions
Set – a collection of items (elements) that have something in common or follow a rule.
Element – individual items in a set
Notation
Set - Italicized Capital letter
Element Italicized Lowercase letters
Elements of a set are listed inside Curly Brackets and separated by commas

3. Each element of a set is unique should be listed more than once
Sets
Each element of a set is unique
So, no element
should be listed more than once
within the set

4. Remember - Each element of a set is unique
Sets
Examples
Possible outcomes for flipping a coin: {heads, tails}
Possible outcomes for rolling a standard 6-sided die {1, 2, 3, 4, 5, 6}
Grade levels at Wando {Freshman, Sophomore, Junior, Senior}
Remember - Each element of a set is unique

5. Venn Diagrams Definition
Venn Diagram– a diagram which uses circles (or other closed shapes) to represent sets.
The universal set is represented by a rectangle.
Individual sets within the universal set are represented by circles (or other closed shapes) within the rectangle.  A U B A

6. Using Sets and Venn Diagrams
Example Problem 1:
We want to look at how many students in a class have at least 1 sister and/or have at least 1 brother.

7. Let’s Create a Venn Diagram Step 1. Draw the Universal Set

8. What is the Universal Set for this example?
U = {all of the students in the class}

9. Step 2. Draw a circle for each possible outcome – they should overlap (We have 2 possible outcomes.)

10. Notice the overlap? This is the called the INTERSECTION.
In this problem, the intersection represents students who have at least 1 brother and at least 1 sister.

11. Question 1 - What does section A represent
Question 1 - What does section A represent? (Click on the correct answer.)
Students with
No Siblings
Students with
Sisters Only (No Brothers)
Students with
Brothers Only (No Sisters)
Students with at least 1 Sister and at least 1 Brother

12. Not Quite While any student with a Sister
goes into the yellow circle, only
those with a sister, but no brother go into the section labeled A. If a student with a sister, also has a brother, the student would go into the section labeled B.

13. That’s right!
Section A represents students with at least 1 sister and no brothers.

14. Students with at least 1 Sister and at least 1 Brother
Question 2 - What does section B represent? (Click on the correct answer.)
Students with
No Siblings
Students with
Sisters Only
(No Brothers)
Students with
Brothers Only
(No Sisters)
Students with at least 1 Sister and at least 1 Brother

15. Not Quite While any student with a Sister
goes into the yellow circle and any student with a brother goes into the red circle, students with both sister(s) and brother(s) go into the intersection of the circles, section B.

16. That’s right!
Section B represents students with at least 1 sister and at least 1 brother.

17. Question 3 - What does section C represent
Question 3 - What does section C represent? (Click on the correct answer.)
Students with
No Siblings
Students with
Sisters Only (No Brothers)
Students with
Brothers Only (No Sisters)
Students with at least 1 Sister and at least 1 Brother

18. Not Quite While any student with a Brother
goes into the red circle, only
those with a brother, but no sister go into the section labeled C. If a student with a sister, also has a brother, the student would go into the section labeled B.

19. That’s right!
Section C represents students with at least 1 brother and no sisters.

20. Question 4 - What does the blue section (Section D) represent
Question 4 - What does the blue section (Section D) represent? (Click on the correct answer.)
Students with
No Siblings
Students with
Sisters Only (No Brothers)
Students with
Brothers Only (No Sisters)
Students with at least 1 Sister and at least 1 Brother

21. Not Quite Any students with a sister go
in the yellow circle and any students with a brother go into the red circle. Students with no siblings go in the outer blue part, section D.

22. That’s right!
The blue section (D) represents the students with no siblings.

23. Notation