Set Theory_ Using Venn Diagrams

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					 Set Theory: Using Venn Diagrams
• Universal Set (U): the set of all elements under
  consideration. www.onlinemathlearning.com/universal-set.com
• #1) U = {prime numbers less than 21}: {2,3,5,7,11}
   A = {odd prime numbers <21}: {3,5,7,11}
   A’ =

   #2) U = {Multiples of 5 that are <50}:
     U = {5,10,15,20,25,30,35,40,45}
   A = {mult. of 10 that are <50}: {10,20,30,40}
   A’ =
Set Theory: Using Venn Diagrams
                       U: Universal Set




     A                      B




Intersection: A   B=
Set Theory: Using Venn Diagrams
                             U: Universal Set




 Universal Set or complement of (A ∩ B)
                     noted as (A ∩ B)’
Set Theory: Using Venn Diagrams
                           U: Universal Set




    A                           B




    Union: A U B =   and
Set Theory: Using Venn Diagrams
                             U: Universal Set




 Universal Set or complement of (A U B)
                     noted as (A U B)’
Set Theory: Using Venn Diagrams
                            U: Universal Set



         A         B




     Complement of A = A’
Set Theory: Using Venn Diagrams
                            U: Universal Set



         B         A




     Complement of B = B’
Set Theory: Using Venn Diagrams
                           U: Universal Set
          A           B




       Empty Set / Disjoint Sets
Set Theory: Using Venn Diagrams
                           U: Universal Set

                 B



             A




           Subset: A  B
Set Theory: Using Venn Diagrams
                           U: Universal Set

                 A



             B




           Subset: B  A
Set Theory: Using Venn Diagrams
• Assignment:
  – Number your paper 1-9.
  – Write the relationship that you see at each
    problem – use set notation!!!
  – Remember that it is quiet in a museum!!!!
• Handout “Venn Diagrams WS” (1-3)
    (half-sheet) and work problems together…
Set Theory: Using Venn Diagrams
   from the Venn Diagram WS (1-3) (half sheet)
                  Gym class = 24
                    students
Set Theory: Using Venn Diagrams
   from the Venn Diagram WS (1-3) (half sheet)
                  Gym class = 24
                    students
Set Theory: Using Venn Diagrams
  from the Venn Diagram WS (1-7) (dog on back)
                           50 students




     Chorus still has 18 and Band still has 26 students.

  CUB=                               C    D=
   Students not enrolled in chorus or band =
Set Theory: Using Venn Diagrams
                          320 students



                   S                      B




  SUB=                                S    B=
   Students not enrolled in chorus or sports =
Set Theory: Using Venn Diagrams
                                        S
  3         F
                                        p
  0         r
                                        a
            e
                                        n
  s         n
                                        i
  t         c
                                        s
  u         h
                                        h
  d
  e
  n
  t
  s
                                Latin




   Students enrolled in French only
Set Theory: Using Venn Diagrams
                       Dog
  3    Cat
  2

  s
  t
  u
  d
  e
  n
  t
  s
                Bird
Set Theory: Using Venn Diagrams
• Homework:
• Venn Diagram word problem worksheet.

				
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posted:11/28/2011
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