2.2 Venn Diagrams and Subsets

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2.2 Venn Diagrams and Subsets Powered By Docstoc
					2.2 Venn Diagrams and
       Subsets
• Venn diagrams (developed by the John
  Venn) are drawings represented by a
  rectangle and oval regions.
  – Rectangle: the universe
  – Oval regions: subsets of the universe
• Universe (represented as U) includes all
  things under discussion at a given time.
  – Ex: When we discuss about the numbers of
    people who can speak Spanish at Loudoun
    campus. The universe can be everybody at
    the school include students, faculties and
    staffs. The subset is the set of people who
    can speak Spanish
• The complement of a set A, symbol A’ (read A
  prime)
  A’ = {x | x Є U and x Є A}

• Ex1): Let U = {1,2,3,4,5}             1,2,4, 3,5
                                        A
           A = {1,2,4}
                                               A’
           A’ = ?
           A’ = {3,5}
Ex2) What is the complement of the empty set?
  {x | x Є U and x Є }
• Set A is a subset of set B (A     B) if every element
  of A is also an element of B
  Ex: {1,2,3}       {1,2,3,4}
         {}        U
      {a, b}       {a, b}

• Set A is equal to set B (A = B) if A   B and B     A
  (**every set is a subset of itself )

• Set A is a proper subset of set B (A     B) if A   B
  and A ≠ B
  Ex: {1,2}    {1,2,3,4}
Ex: Find all possible subsets of each set
1) { }
Subset is:
2) {a}
Subsets are:
3) {a, b}
Subsets are:
4) {a,b, c}
Subsets are:
If a set has 0 element - we have 1 subset
             1          -        2
             2         -         4
             3         -         8
             4         -         ?
             n         -         ?

Therefore:
if a set has n element, there are 2n subsets
or 2n - 1 proper subsets

				
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