1. Based on the diagram, what is the total number of students who did participate in volleyball? Warm-Up: Baseball Basketball Volleyball

Set Theory

Vocabulary A set The elements Subsets Empty set/Null set Universal set of a set are the objects in a set. is any well defined collection of “objects.” consists of elements from the given set. is the set that contains no elements. is the set of all possible elements. *Make sure you leave a few empty line under each word & definition to provide examples and/or illustrations

Ways of Describing Sets List the elements Give a verbal description “A is the set of all integers from 1 to 6, inclusive” Give a mathematical inclusion rule

Some Special Sets The Null Set or Empty Set. This is a set with no elements, often symbolized by or {} The Universal Set. This is the set of all elements currently under consideration, and is often symbolized by U

Universal Sets The universal set is the set of all things pertinent to a given discussion and is designated by the symbol U Example: U = {all students at Brandeis} Some Subsets: A = {all Computer Technology students} B = {freshmen students} C = {sophomore students}

What?!? Find the Subsets What are all the subsets of {3, 4, 5} {} or Ø {3}, {4}, {5} {3,4}, {3,5}, {4,5} {3,4,5}

Try it with a partner Page 197 (20, 21)

Venn Diagrams Venn diagrams show relationships between sets and their elements Universal Set Sets A & B

Venn Diagram Example Set Definition {1, 2, 3, 4, 5, 6, 7, 8} U =

Set Complement ~A or A′ “A complement,” or “not A” is the set of all elements not in A. *What the others have that you don’t*

Practice: U black purple A red white blue green Types of color Universal set U = What is the complement of set A?

More Practice: U = {1, 2, 3, 4, 5} is the universal set and A = {2, 3}. What is A′? U = {a, b} is the universal set and T = {a}. What is T′? U = {+, -, x, ÷, =} is the universal set and A = {÷, =}. What is A′?

Try it with a friend Page 197 (26, 27) Page 198 (39)

Venn Diagrams Here is another one A B What is the A′?

A moment to Breath

The moment is over

Combining Sets – Set Union “A union B” is the set of all elements that are in A, or B, or both. This is similar to the logical “or” operator.

Combining Sets – Set Intersection “A intersect B” is the set of all elements that are in both A and B. This is similar to the logical “and”

Venn Diagrams Venn Diagrams use topological areas to stand for sets. I’ve done this one for you. A B AB 

Venn Diagrams Try this one! A B AB 

Examples

Try it on your own! Let P = {b, d, f, g, h}, M = {a, b, c, d, e, f, g, h, i, j}, N = {c, k} P M P  M P  N N  M P  N 

Try it on your own! Page 218 (10, 12, 14, 16, 18, 20)

Product?!? Given set D and F, find D x F D = {1, 3, 5}, F = {0, 2} Given set R and S, find R x S R = {Bob, Rose, Carlos}, S = {Sheila}

Pair in-class-mini-project Please pick a student with whom you KNOW you CAN work and be PRODUCTIVE Assignment: Develop/Create a book explaining all four Vocabulary words from the SET THEORY topic (Complement, Union, Intersection, Product). Use a self-created example for each concept. Your audience - a group of elementary students who learn better when the teacher utilizes images/drawings. Be creative!!! Make sure your work makes sense, you might have to present it!

Wrap-Up: Summary Home-Learning Assignment #2: Page 198 (46) Page 199 (53) Page 219 (22) Page 220 (40, 46)