1. Based on the diagram, what is the total number of students who did participate in volleyball?

15 9 11 6 5 4

12

15 9 11 6 5 4

12

Warm-Up:

Baseball Basketball

Volleyball

Set Theory

VocabularyA 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

A= 1,2,3,4,5,6

A= Integers 1 6x x

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 discussionand 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

1 3

5 8 2 4

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.

A B

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”

A B

Venn Diagrams

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

A B

A B

Venn Diagrams

Try this one!

A B

A B

Examples

{1,2,3}A {3,4,5,6}B

{3}A B

{1,2,3,4,5,6}A B

•

•

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

PN

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:

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