Introduction to Set Theory - PowerPoint

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Introduction to Set Theory - PowerPoint Powered By Docstoc
					              Warm-Up:
1. Based on the diagram, what is the total number of
students who did participate in volleyball?




         15          9       11

                     6
               5             4

                     12

                Volleyball
Set Theory
*Make sure you leave a few empty line under each word & definition to
                provide examples and/or illustrations

                     Vocabulary
 A set is any well defined collection of “objects.”

 The elements of a set are the objects in a set.

 Subsets consists of elements from the given set.

 Empty set/Null set is the set that contains no elements.

 Universal set is the set of all possible elements.
Ways of Describing Sets
List the elements

       A= 1,2,3,4,5,6
Give a verbal description
  “A is the set of all integers from 1 to 6,
  inclusive”
Give a mathematical inclusion rule
    A= Integers x 1  x  6
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
                      Sets A & B



                                       Universal Set


          5       8           2    4
              1       3
Venn Diagram Example
           Set Definition
 U=   {1, 2, 3, 4, 5, 6, 7, 8}
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:
                      Types of color
      U
             black

            purple    A                red

             white          blue             green



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 B
“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 B
“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




             AB
Venn Diagrams
Try this one!

   A                  B




                AB
       Examples

        A  {1,2,3} B  {3,4,5,6}

•   A  B  {3}

•   A  B  {1,2,3,4,5,6}
                 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)

				
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posted:10/4/2012
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