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Click to edit Master title style=
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Sets
Chapter 2
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Set Concepts
Section 2.1
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Set Theory
pSet Theory:=   Used to organize and categorize things, and thus better describe them = ;
pSet:  A collection of objects
pElements:=   Objects within a set
pWell-Defined Set:  Set in which the elements can be = clearly determined<= /div>
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Two Methods to Describe a Set=
pRoster Form
pSet-Builder Notation
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Roster Form
<= span style=3D'font-family:"Times New Roman"'>pUses braces to enclose the elements of a set
pEllipsis:
nThree dots (…) that indicate that the elements of a set continue in the same pattern
nAn ellipsis followed by a last element indicates that the set continues in the same pattern up to and including the l= ast element
pInclusive:=   Indicates that the “end” elements are included in a set
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Examples:  Write the following set= s in Roster Notation
<= span style=3D'font-family:"Times New Roman"'>pSet of Natural Numbers
n{1,2,3,…}
pSet of Odd Natural Numbers
n{1,3,5,…}
pSet of natural numbers between 1 = and 5
n{2,3,4}
pSet of natural numbers between 1 = and 5, inclusive
n{1,2,3,4,5}
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Examples:  Write the following sets= in = Roster Notation
pSet of all the letters of the alphabet
n{a,b,c,…,z}
pSet of the letters a, b, and c
n{a,b,c}
pSet of the letters between d and h
n{e,f,g}
pSet of the letters between f and x, inclusive
n{f,g,h,…,x}
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Set-Builder Notation
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>p
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>p
pA      =3D      {      x         |      Condition(s)   &nbs= p; }
Set A
the set of
all elements x
such that
is
x meets these conditions
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Examples
p Read the following sets in set-builder notation.  Then <= /span>express the sets in roster notation
pA =3D { x | x ε N and x > 5 }
nA =3D {6,7,8,…}
pB =3D { x | x ε N and x < 5 }
nB =3D {1,2,3,4}
pC =3D { x | x ε N and 3 ≤ x < 10 }
nC =3D {3,4,5,…,9}
pD =3D { x | x ε N, x is odd, and x > 100}
nD =3D {101,103,105,…}
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Examples
pConvert the follow= ing sets, given in roster notation, to set-builder notation.  Then read the sets in set-builder notation.
<= span style=3D'font-family:"Times New Roman";font-size:114%'>pE =3D {-2,-1,0,1,2= }
nE =3D { x | x ε Z and -3 <= ; x < 3 }
pF =3D {11,12,13,…,25}
nF =3D { x | x ε N and 10 <= ; x < 26 }
<= span style=3D'font-family:"Times New Roman";font-size:114%'>pG =3D {10,12,14,16,18,20,…}
nG =3D { x | x ε N, x is even= , and x ≥ 10 }
pH =3D {1,2,3,…}
nH =3D { x | x ε N }
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Equality of Sets
pA =3D B if and only if set A and = set B have exactly the same elements
pExample:=   If A =3D {1,2} and B =3D {2,1}, then A =3D B
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Cardinal Number of a Set
pCardinality or n(A):=   Number of elements of set A
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Examples:  Find the cardinalities of = the following sets
<= span style=3D'font-family:"Times New Roman";font-size:86%'>pSet of natural numb= ers between 1 and 5
n3
pSet of natural numb= ers between 1 and 5, inclusive
n5
pSet of all the lett= ers of the alphabet
n26
pSet of the letters = a, b, and c
n3
pSet of the letters between d and h
n3
pSet of the letters between f and x, inclusive
n19
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Equivalency of Sets
pSet A is equivalent to set B if a= nd only if
n(A) =3D n(B)
pNote:  Equal sets are always equivalent,= but equivalent sets are not always eq= ual
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Examples:  Determine if the fol= lowing sets are equivalent
pA =3D {red, blue, yellow, green}
B =3D {1,2,3,4}
nYes, n(A) =3D n(B) = =3D 4
p <= /span>
pC =3D {Pirates, Steelers, Penguins}
D= =3D {hockey, baseball, football}
nYes, n(C) =3D n(D) = =3D 3
p <= /span>
pE =3D {France, England, Germany}
F= =3D {London, Rome, Berlin, Paris}
nNo, n(E) =3D 3, n(F= ) =3D 4
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Finite Set
pSet A is finite if n(A) =3D 0 or = if n(A) is a natural number
pA set that is not finite is said to be infinite
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Null Set (Empty Set)
pThe set that contains no elements
pSymbolized by { } or Ǿ <= /span>
pNote:  The set {0} is not the same as th= e null set
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Universal Set
pThe set that contains all the elements for any specific discussion
pSymbolized by U
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Examples
pIndicate the set of states that b= egin with Z
pWhat is the universal set for the above question?
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Subsets
Section 2.2
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Subsets
pSet A is a subset of set B if and only if every element of A is also an element of B
pSymbolized 
------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0141_image012.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBoYGxgZOIEsYTjGBmADOa5QDYTgwxYlhWIOZlgLCZGRiiLken///9g lh6jBFSMG66OhwlkqhCQpcbGzyDF8B+kmEEAyD8AZKkBaQegQcuAmBuqhofBN7EkI6SyIBUoB7b7 N1PDP4gLJzCCHcTEIBBcmZuUn8NQ7gAUKGXjurj96PHyA0CscOBUOQODAQMLUFwXqJoDSBtxMTCa MIC0nq3kgtrCBXYJI9hUiB0CDOxg3h6w2xmZmJSCK4tLUnNBPC4GRYYusGKQrimfhRh2HjxeDrGD EWzXB6AsM1g/ABrdHd1QAQAA ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0141_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABgAR ABAAgAAAAAAAAAIghBGpq5YHo5P0hEovlnrD7k3hN1qlBY7M+pzu67ByUAAAOw== ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Chapter 2 Presentation
Examples
pDetermine whether set A is a subset of set B.  If it is not a subset, prove such (find an element in set A that is not in set B).
pA =3D {10,12,14,…}
B =3D {2,4,6,…}
nA     B
p <= /span>
pA =3D {x | x ε N and x is odd}
B= =3D {x | x ε N and x > 10}
nA     B
1= ,3,5,7,9 are elements in set A and not in set B
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Examples (cont.)
pA =3D {1,2,3,…,10}
B =3D {x | x ε N and 0 < x < 11}
nA     B
In fact, A =3D = B
p <= /div>
pA =3D {   }
B =3D {3,4,9}
<= span style=3D'font-family:"Times New Roman"'>nA     B
In fact, the null set is a subset of every set (even itself)!
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Proper Subset
pSet A is a proper subset of set B= if and only if A   B and A ¹ B (there is an element in B not in A)
pSymbolized
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Examples:  Determine whether
set A is a proper subset of set B
pA =3D {4,6,8,…}
B =3D {2,4,6,…}
nA     B
p <= /span>
pA =3D {1,2,3,4,5}
B= =3D {5,4,3,2,1}
nNo, A =3D B
p <= /span>
pA =3D {x | x =3D 10}
B= =3D {x | x ≥ 10}
nA     B=
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Differences Between an
“Element of” a= nd a “Subset of”
pFor ☺ to be= an Element of a Set:

  ☺    { ☺ }
Element must be here
Element must be here within braces=
------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0428_image023.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBwYHRgZOUEsUTiGBmADOa5QDYTgwxYlhWIOZlgLCZGRiiLken///9g lh6jBFSMG66OhwlkqhCQpcbGzyDF8B+kmEEAyD8AZKmBlAENSgNibqgaHgbfxJKMkMqCVAYGBbDd v5ka/kFcOIER7CAmBoHgytyk/BwGBiturt0uT4UYbsz/XP4QiBUUvpabsad1sgAV6gJVcwBpIy4G RgGQNQznKrmgtnCBXcIINhVihwADO5i3B+x2RiYmpeDK4pLUXAYGkHkMQB2KDF1gDSCdCc+FGCB2 MILpD0AZZrB+AAMEzG1QAQAA ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0428_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABQAK AAoAgAAAAAAAAAIRhIMZgOa+HpRP2UZPnhv3WwAAOw== ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0428_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhWQBHAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgBX AEMAgQAAAAAAAP///wECAwLbhI+py90RnJy02gRzvLx7qW3fSHZZiaYgAKnuyx4iTJtzjXNtzl97 D1wFhw+iUXE7Dn/KkPMJjUqn1KpTgM1qt9yu9wsOi72BsfmMTofL6rb73WXD5/SzvI7Pb+/6fp3v F+gGKFhoZ4iYRpjIyLXYCCnwGMk4SYloeVmYqRnI2dn3CZonOvpnClmKCqe6Ouia2AqrOGsoW2t2 iyumuwvW60sWHDqsB1ysdYyMpbzcjPxcHD08HVzte72bjbtd2z37DRvuOr5ajnpumj66Dtre+a4Z f2lVb3+PD1UAADs= ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0428_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYQBCAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgBe AD4AgQAAAAAAAP///wECAwLmTICpy+0Po5zA2EOz3tzdDobi843muRkIhrZupL7ynMT0jdr4Lur8 n2IBhxMf8egRIneXpvMJjUqn1KqxIshqt9yu9wsOi8dfJZaMTqvXYXOADY/Ly4z3/I5Xu/P8Pn1h 5yfYtzdoiFd4qAiXuOiI1vgoCRY5ablVeXmZqTnJ2fn4CbooOnpYajqImuq3ysrn+opYJysZWyt3 i8tIu6uo66vXG6w6TNxqfAybrDwL2Iz8DL0sPe2sEGg9B6zdxd2NyQwuXD3O9m2OPq4Ozt7trg1v LT9ND23fjK+sf+xm9Q8woMAnBQAAOw== ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0430.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Chapter 2 Presentation
Differences Between an
“Element of” a= nd a “Subset of”
pFor ☺ to be= a Subset of a Set:

  {☺}    { ☺ }
Element must be here within braces=
Element must be here within braces=
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Differences Between an
“Element of” and a “Su= bset of”
<= span style=3D'font-family:"Times New Roman"'>pExamples:  Determine if the following are Tr= ue or False
p1   {1,2,3} <= /div>
nTrue
p{1}   {1,2,3} <= /div>
nFalse
p1   {{1},{2},{3}}
nFalse
p{1}   {{1},{2},{3}}
nTrue
n
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Examples (cont.)
<= span style=3D'font-family:"Times New Roman"'>p1   {1,2,3}
nFalse
p{1}   {1,2,3} <= /div>
nTrue
p1   {{1},{2},{3}}
nFalse
p{1}   {{1},{2},{3}}
nFalse
p{{1}}   {{1},{2},{3}}
nTrue
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Consider
4 =3D 22
{   }= , {a}, {b}, {a,b}
{a,b}
2 =3D 21
{   }= , {a}
{a}
1 =3D 20
{   }=
{   }=
Number of <= /span>Subsets
Subsets
Set
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Number of Subsets
pNumber of Distinct Subsets of a Finite Set
=3D 2n,where n is the number elements in the set
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Example
pDetermine the number of distinct subsets for the set {a,b,c}.  List them.  How many are proper subsets? =
p23 =3D 8
p{a,b,c} {a,b} {a} <= /span>{   }
 {a,c} {b}
 {b,c} {c}
p7 are proper subsets
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Example
pDetermine the number of distinct subsets for the set {w,x,y,z}.  List them.  How many are proper subsets? =
p24 =3D 16
p{w,x,y,z} {w,x,y} {w,x} {w} <= /span>{   }
<= span style=3D'mso-tab-count:2;width:19.23%'> {w,x,z} {w,y}= {x}
<= span style=3D'mso-tab-count:2;width:19.23%'> {w,y,z} {w,z}= {y}
<= span style=3D'mso-tab-count:2;width:19.23%'> {x,y,z} {x,y} = {z}
<= span style=3D'mso-tab-count:4;width:42.91%'> {x,z}
<= span style=3D'mso-tab-count:4;width:42.91%'> {y,z}
p15 are proper subsets
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Venn Diagrams,
Set Operations
Section 2.3
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Venn Diagrams
pMethod of visually representing elements of sets
pUniversal set is shown as a recta= ngle
pOther sets under consideration shown as circles within the rectangle
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One Set in a Venn Diagram
= pSet A in a Venn diagram
U
A
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Two Sets in a Venn Diagram
pThere are four possibilities: = ;
pCase 1:  Disjoint Sets <= /div>
pCase 2:  Subsets
pCase 3:  Equal Sets
pCase 4:  Overlapping Sets
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Case 1:=   Disjoint sets
pSet A and set B share no <= /span>elements
pThere is no overlap of the circles
U
A
   B
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Case 2:=   Subsets
pA  B
pAll elements in set A are in = set B
pCircle A is entirely enclosed in circle B
U
A
  B
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Case 3:=   Equal Sets
pA =3D B
pSet A and set B contain the = exact same elements
pA and B are represented by = the same circle
U
A
   B
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Case 4:=   Overlapping Sets
pSet A and set B have some = = elements in common
pCircle A and circle B overlap
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>p
     A
B
U
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Standard Two Set Venn Diagram=
pVenn diagram is always drawn the same
pWe then place the elements in the appropriate regions
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Two Set Venn Diagram
with Regions Labeled
U
B
III
     A
I
II
IV
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The Four Cases with a Standard = Venn Diagram
pCase 1:  Disjoint Sets <= /div>
pCase 2:  Subsets
pCase 3:  Equal Sets
pCase 4:  Overlapping Sets
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Case 1:=   Disjoint Sets = ;
pLet U =3D {1,2,3,4,5}
A =3D {1,2}
B =3D {3,4}
pRegion II is empty<= /div>
U
B
     A
1,2
3,4
5
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Case 2:=   Subsets
pLet U =3D {1,2,3,4,5}
A =3D {2,3}
B =3D {2,3,4}
pRegion I is empty
U
B
     A
2,3
4
1,5
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Case 3:=   Equal Sets
pLet U =3D {1,2,3,4,5}
A =3D {3,4,5}
B =3D {3,4,5}
pRegions I and III are empty
U
B
     A
3,4,5
1,2
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Case 4:=   Overlapping Sets
pLet U =3D {1,2,3,4,5}
A =3D {2,3}
B =3D {3,4,5}
pNo regions are empty
U
B
     A
2
4,5
1
3
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Set Operations
pMathematical tools to work with sets
pSimilar to how the operations +, -, x, ¸ give us tools to work with numbers
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Complement
pAll elements in the universal set that are not in the given set
pSymbolized A’
pRegions III and IV together
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Examples of Complement
<= span style=3D'font-family:"Times New Roman"'>pGiven U =3D {a,b,c,d,e,f}
A =3D {a,b,c}
B =3D {b,c,d,e}
C =3D {   }
pFind A’ <= /div>
n{d,e,f}
pFind B’ <= /div>
n{a,f}
pFind C’ <= /div>
n{a,b,c,d,e,f}
A’=3D{d,e,f}
B’=3D{a,f}
C’=3D{a,b,c,d,e,f}

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Intersection
pThe intersection of set A and Set= B is the set of elements common to A and B
pSymbolized A ∩ B
pRegion II
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Examples of Intersection
pGiven U =3D {a,b,c,d,e,f}
A =3D {a,b,c}
B =3D {b,c,d,e}
C =3D {   }
pFind A ∩ B
n{a,b,c} ∩ {b,c,d,e} =3D {b,c} =
pFind A ∩ C
n{a,b,c} ∩ {   } =3D {   }
A ∩ B =3D {a,b,c} ∩ {b,c,d,e} =3D {b,c}
A ∩ C =3D {a,b,c} ∩ {   } =3D {   }
A’ ∩ B =3D {d,e,f} ∩ {b,c,d,e} =3D {d,e}
(A ∩ B)’ =3D {b,c}’ =3D {a,d,e,f}
A ∩ U =3D {a,b,c} ∩ {a,b,c,d,e,f} =3D {a,b,c}
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Examples of Intersection (cont.)
<= span style=3D'font-family:"Times New Roman"'>pFind A’ ∩ B
n{a,b,c}’ ∩ {b,c,d,e}
n{d,e,f} ∩ {b,c,d,e}
n{d,e}
pFind (A ∩ B)’
n({a,b,c} ∩ {b,c,d,e})’&#= 13;
n{b,c}’
n{a,d,e,f}
pFind A ∩<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> U
n{a,b,c} ∩ {a,b,c,d,e,f} =3D {a,b,c}= <= /div>
<= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-4.43%;font-family:Wingdings;font-size:75%'>p<= span style=3D'mso-special-format:lastCR;display:none'>
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Union
pThe union of set A and set B is t= he set of elements in A or B or both
pSymbolized A   B
pRegions I, II, and III together
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Examples of Union
pGiven U =3D {a,b,c,d,e,f}
A =3D {a,b,c}
B =3D {b,c,d,e}
C =3D {   }
pFind A   B =
n{a,b,c}   {b,c,d,e} =3D {a,b,c,d,e} <= /div>
pFind A   C =
n{a,b,c}   {   } =3D {a,b,c}
{a,b,c}  {b,c,d,e} =3D {a,b,c,d,e}=
{a,b,c}  {   } =3D {a,b,c}
{d,e,f}  {b,c,d,e} =3D {b,c,d,e,f}=
{a,b,c,d,e}’ =3D {f}
{a,b,c}  {a,b,c,d,e,f} =3D {a,b,c,d,e,f}<= /font>
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Examples of Union (cont.)
pFind A’   B =
n{a,b,c}’   {b,c,d,e}
n{d,e,f}   {b,c,d,e} =3D {b,c,d,e,f} <= /div>
pFind (A   B)’
n({a,b,c}   {b,c,d,e})’
n{a,b,c,d,e}’ =3D {f}
pFind A   U =
n{a,b,c}   {a,b,c,d,e,f} =3D {a,b,c,d,= e,f} <= /div>
p
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Relationship of n(A  B), n(A), = n(B), and n(A ∩= B)
pConsider A =3D {a,b,c} and B =3D {b,c,d,e}
pn(A) =3D 3 n(B) =3D 4 What is n(A  B)?
pn(A  B) is no= t 3 + 4.  It is  3 + 4 – 2 =3D 5 =
pFor any finite sets A and B:
n(A  B) =3D n= (A) + n(B) – n(A ∩ B)
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Example
pSet C has 10 elements
Set D has 14 elements
There are 6 elements common to the two sets
pFind the number of elements in C   D
p10 + 14 – 6 =3D 18
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Venn Diagrams with
3 Sets
Section 2.4
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Venn Diagram with 3 Sets
pShows three sets, represented by circles
pThere are areas for the elements that reside only in each individual sets (regions I, = III, VII)
pEach circle has an area of intersection with every other circle (regions II, IV, VI)
pThere is an area for the intersection of all three sets (region V)
pThere is an area for elements in none of the sets (region VIII)
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3 Set Venn Diagram
I
II
III
IV
V
VI
VII
VIII
U
A
B
C
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3D"Venn
I
II
III
IV
V
VI
VII
VIII
U
A
B
C
3 Set Venn Diagram
pA ∩ B ∩ C V
pA ∩ B <= /span>II,V
pA ∩ C <= /span>IV,V
pB ∩ C <= /span>V,VI
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3 Set Venn Diagram
pA U B I,II,III,IV,V,VI
pA U C I,II,IV,V,VI,VII
pB U C II,III,IV,V,VI,VII
pA U B U C
 I,II,III,IV,V,VI,VII
p(A U B U C)’ VIII
I
II
III
IV
V
VI
VII
VIII
U
A
B
C
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Constructing a Venn Diagram
= pStart in the middle (region V) and work outward
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Example:  Create a Venn diagram usi= ng the following sets
= pU =3D {1,2,3,4,5,6,7,8,9,10}
A =3D {2,4,6,8,10}
B =3D {2,5,8}
C =3D {5,6,7,8,9,10}
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Example
3D"Venn
U
A
B
C
------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0421_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh4gFuAXcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALEIAGgBh ARYBgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7A4TiSJbmiabqyrbuC8fyTNf2jedGzvf+DwwKh8Ri amdMKpfMpvOpC0Cn1Kr1inUhs9yu9wuubcPksvlcHaPX7LZbLH3L5/S6uo7P67P3vf8PSNQXSFho GDN4qLjICJDYCBmp9yhZaclGeam56ZXJ+QkK5RlKWioYZ5qqajS66vr60go7S1sim6qRl1EbcvsJ cQJ8Jmz7AOtryYCz8MV842yKDKkwRJ2WUI1NKr2I0OT9BL6kzcldSO6EfgoyJX5pDuh+Db8iT2U/ jbqJb8Vv4z8vmT6B9IoAhHHwCrt8mhYOcygjIReIhwrKofhwYCyL/98wBuKICWS4Wx7XlPQj0oxE lSdHtDSZskvMMC/btKwZUiNKnYRw2kzk8+c5nn+Cvukzk0/Se0T3GL245enRpaKa6qI6cYdUqFbd YGVaaeXOsT27ljX7Ee3DsgS/NlNbxm1HgSLkyoRLE+/asAPtZsXjl5XeSToDYzHsA7EQxQFNMAY7 53HiwVebSq4amXKnyyNVbAWs+RphuvVC0/kM2Y7pzFpWQ50KmnRr2TBVv9PLOZ1rJrlp9OY9+Pe4 3cNPExc6Q7gS5UeOz032z3ltNMxbVDdo+rrB6V6lU3etPdv3i7d1lGcJmy+P8Iu9A2Ff7N1k2mDg k7D/QyT++XHdi/+Hnp9//Q0YEn1RGHhXgQC+JyAZ2u23Xw9JRbheg89YKCGG9QlI4YEbchcJVR0u o2FyJS5zXjUpJriXJF+NeOGHLYaIIYzRyajSiioi2M+JcPDIIJCpOeijUssVycdbw8g3jo4KIYkI lD0CJyRmBLroo40/suigk9staCSRTFKp3l9ilkkmllziSKNuVbrZ5ZtBSNnPmpuN+ZyaYbIZopV6 HkYnC1r6JuWgJprJZyOKGRpRoPHlJeecjraDaDNeLofnlDRl+s2lnSWq6JAMAQopmHD+qamSaH6K qmigdhMoo1Hueeeqp7ZJ6quKPCYrQpPW9WswwebJKq5PltoqsaP/HqtrRbEOm2aqtSYb7bLS2qno s5EmcV2vG4maLa3YMsIrtMXlqiq156pb7LiwgkvusN2a22Q79HIr77296MsKvO+ia6mpnW4rWJy2 8sapvwBb61guniVs75nJOiBoA4+y2667u6JiDYnaeDubuBo7q06AJcdb6bT5GCYWWQt3sjJq0bUc m8gjO7UQyxzLbNLN18YDkc738Xzlyz5nNgiSSBHdbMYwp2VZOs2B7Ii57Hn7kl+ZMD2Ryk3nZF2W aHH9c9lHZxRLtVOPdnYaoOF2Itz8apGuxFMFVyIyZN9qs9dgJ3ckoaz5/XXdjRYMx9wo6GsfhfS8 uNreiBNueH+7/9UIHoSMK+4S5/sSJyLojfOLH3xkh56h5/MqmJd0E7p+td3otR6kpLYjW3nRWfk3 E+/d6j475R7yJ+m94TmeO/HrYZd837KbrTyJkxvddsoKB1hh4EkGz7qr+GavPfTWjyd+7TeqzTfu 3fu5ruDoK6v++vB/v+X87QMvf/jph+w0/eS/1j/9fYt97yvc86YXwOZ4737cAyAD96fA8mEPObYR YMTCRr32dOcqFrTX2PLVwQYOjnnO69z4zEfBmv3nhMASHvjSwzYNCo85qBthDCeYu9XdzoY3zJDs HuQeydnPOLALnhCj5zEV7sQ5ppPCEZE4Mw5CTUIwGV2FPFcxQ/9YpHRcjAIWs6jFzI2ndEnE2cbO Z8QmotGMG9PM1dTwRB+a6IsDbOOhiFSY2DWKjnX8Vx+bty/8eYZqgVzZH3dXMdLBJY7MMqR1aBe2 6qiFkY2kkVmMpzcadoWSGWyjZayGGk76apB8rF9bhKWUgtDsFIsjZCt/QZFgrZKUsiyGKyMIyzFM apaR3OXObjnIUnijXJATJSp5yUZhInNmgVlm4oCJwVWcjEHGFJYze1nKFeLic5Lr2JOuaUt2ZFOG quiLMnwFjQ15E5vygCb/ovFJDnBFnqgEhTvv2BqKDUWf79zHOBHIizX6U5r/NE4o7nm4gC7PngVl pULNw1CCPhT/orCU6ESfcdCG7uii/8ioNDmK0YiWE6QC9VQ5SGrKhmh0MSh1XzlWOqeWAk6k25Qp IjxaTph6Bae40KlNeApPmyIEqMoUatpoGlSjgrGiOVXqUl9qUafiEqpNlepUB/pRq74SqdHQ6uK2 4VMcetUlYHUFQjuJMaqOtYVELepa2crVrr61F26N6ljP+tSezhWvpTnGXsMao1cAdlN1tatV+dpX wQ7WhQSDmFEXW1K9ahWxiVWsVykbzFlglltVPQZkJdjYhhz2syk1K2kJWFZabFabhfXsY09bWtO+ Vra8WG1+LFtb2Iawra5FqW0rW4vfSg+3ARVubJOqUOPik7bJ/9XtDonb3IkqN7MPnW4/mVtd575Q s9pFYW+D213vYpe7JLVuPXPr2/DOKrrpHS94ZWreqql3uC21bjWLMt/itba4+dVvXPn72v7C9aLx jaJK26vU+6ayvgLORngVPJTRahfCEZ6sbilcYQuTtsDHDfBZnMrhyQAWw2f8K0zBadi7DorEKJsr sMbJ4nC5+MV8jLGMZ0xjtP0Vx+GEpItDPJzfoDi7PG7lZYYs3Qa/RWc2VmuRp0bJafIYyD1Csnyb vN8nJ3KdUOaylof25WdiIMzRJPMVqSxIM6v5gmtu8wLdDOchxnnO5KSznR165zw/V898Hl6f/xxZ QAv6uoMuNDBwDY3oqyZ60WBmtKMb/ehIoznS+aO0oSdt6RllGtEf6LSnPw3qUIt61KQutakNUAAA Ow== ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0358.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Chapter 2 Presentation
Example:  Create a Venn diagram usi= ng the following sets
= pU =3D {a,b,c,d,e,f,g,h,i,j,k,l} A =3D {a,b,c}
B =3D {a,c,e,g,i,k}
C =3D {a,d,g,j}
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Example
U
A
B
C
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Equality of Sets
pUsed to determine whether stateme= nts (sets and operations) are equal for all sets
pWe use regions to determine potential equality, regardless of the contents of the sets
pIf both statements represent the same regions, then the statements are equal for all = sets
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Example:  Determine whether
(A ∩ B)’ =3D A’ U B’= ; for all sets
Regions
Set
Regions
Set
A’ U B’
(A ∩ B)’
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Example:  Determine whether
 A U (B ∩ C) =3D (A U B) ∩ (A U C)
Regions
Set
Regions
Set
(A U B) ∩ (A U C)
A U (B ∩ C)
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De Morgan’s Laws
pFor all sets A and B,
n1) (A U B)’ =3D A’= ∩ B’
n2) (A ∩ B)’ =3D A&= #8217; U B’
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Example:  We have verified Law 2.<= span style=3D'mso-spacerun:yes'>  Verify Law 1 is true for all sets= .
Regions
Set
Regions
Set
A’ ∩ B’<= /div>
(A U B)’
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Applications with Sets
Section 2.5
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Country-Western Songs
= pCountry Western songs emphasize t= hree basic themes: love, prison, and trucks.  A = survey of the songs played frequently by a local Country-Western radio station produced the follow= ing data:
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Country Western Songs (cont.)=
<= span style=3D'font-family:"Times New Roman"'>n2 songs about truck drivers who are in love while in prison
n10 songs about prisoners in love
n11 songs about truck drivers in love
n7 songs about truck drivers in prison
n23 songs about people in love
n22 songs about truck drivers
n22 songs about prisoners
n3 songs about people who are not in prison, are not in love, <= span style=3D'position:absolute;top:74.5%;left:14.04%;width:79.96%;height:5.25%= '>and do not drive trucks
n
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Country Western Songs (cont.)=
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Country Western Songs (cont.)=
<= span style=3D'font-family:"Times New Roman"'>a)How many songs were surveyed?
b)How many songs were about truck drivers who are not in prison?
c)How many songs were about people = in prison who are not in love and do not drive trucks?
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A Farmer’s Pigs
pA farmer has 36 pigs.  A survey of these pigs produced the following data: =
n16 healthy pigs
n18 fat pigs
n18 greedy pigs =
n11 fat pigs that are also greedy&= #13;
n8 healthy fat pigs
n4 pigs that are healthy and greedy
n3 pigs that are fat, greed, and healthy
------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/slide0427.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Chapter 2 Presentation
A Farmer’s Pigs
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A Farmer’s Pigs
<= span style=3D'font-family:"Times New Roman"'>a)How many pigs have none of the three attributes?
b)How many pigs are greedy but neit= her fat nor healthy?
c)How many pigs are fat and healthy= but not greedy?
d)How many pigs possess exactly two= of the three attributes?
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A’=3D{d,e,f}
B’=3D{a,f}
C’=3D{a,b,c,d,e,f}
A ∩<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> B =3D {a,b,c} ∩ {b,c,d,e} =3D {b,c} <= /div>
A ∩<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> C =3D {a,b,c} ∩ {   } =3D {   }
A’ ∩ B =3D {d,e,f} ∩ {b,c,d,e} =3D {d,e} <= /div>
(A ∩<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> B)’ =3D {b,c}’ =3D {a,d,e,f}
A ∩<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> U =3D {a,b,c} ∩ {a,b,c,d,e,f} =3D {a,b,c}=
{a,b,c}  {b,c,d,e} =3D {a,b,c,d,e}
{a,b,c}  {   } =3D {a,b,c}
{d,e,f}  {b,c,d,e} =3D {b,c,d,e,f}
{a,b,c,d,e}’ =3D {f}
{a,b,c}  {a,b,c,d,e,f} =3D {a,b,c,d,e,f}
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1,1),new hrefList("slide0261.htm",1,-1,1),new hrefList("slide0264.htm",1,-1= ,1),new hrefList("slide0265.htm",1,-1,1),new hrefList("slide0267.htm",1,-1,= 1),new hrefList("slide0269.htm",1,-1,1),new hrefList("slide0273.htm",1,-1,1= ),new hrefList("slide0277.htm",1,-1,1),new hrefList("slide0281.htm",1,-1,1)= ,new hrefList("slide0285.htm",1,-1,1),new hrefList("slide0286.htm",1,-1,1),= new hrefList("slide0287.htm",1,-1,1),new hrefList("slide0291.htm",1,-1,1),n= ew hrefList("slide0292.htm",1,-1,1),new hrefList("slide0431.htm",1,-1,1),ne= w hrefList("slide0298.htm",1,-1,1),new hrefList("slide0299.htm",1,-1,1),new= hrefList("slide0432.htm",1,-1,1),new hrefList("slide0305.htm",1,-1,1),new = hrefList("slide0311.htm",1,-1,1),new hrefList("slide0314.htm",1,-1,1),new h= refList("slide0353.htm",1,-1,1),new hrefList("slide0354.htm",1,-1,1),new hr= efList("slide0355.htm",1,-1,1),new hrefList("slide0356.htm",1,-1,1),new hre= fList("slide0325.htm",1,-1,1),new hrefList("slide0326.htm",1,-1,1),new href= List("slide0421.htm",1,-1,1),new hrefList("slide0358.htm",1,-1,1),new hrefL= ist("slide0422.htm",1,-1,1),new hrefList("slide0372.htm",1,-1,1),new hrefLi= st("slide0373.htm",1,-1,1),new hrefList("slide0423.htm",1,-1,1),new hrefLis= t("slide0385.htm",1,-1,1),new hrefList("slide0424.htm",1,-1,1),new hrefList= ("slide0394.htm",1,-1,1),new hrefList("slide0396.htm",1,-1,1),new hrefList(= "slide0397.htm",1,-1,1),new hrefList("slide0426.htm",1,-1,1),new hrefList("= slide0425.htm",1,-1,1),new hrefList("slide0398.htm",1,-1,1),new hrefList("s= lide0427.htm",1,-1,1),new hrefList("slide0400.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="us-ascii" Chapter 2 Presentation ------=_NextPart_01C90DD7.BEE331E0 Content-Location: file:///C:/6E4BB24E/chapter_2_presentation_files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
 No= tes
Slide Show
Outline
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