2-3-4- Graphs and Trees (part 1)

2-3-4- Graphs and Trees (part 1) - c ElementarySetTheory

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c © Jalal Kawash 2009 Peeking into Computer Science Click to edit Master subtitle style  10/11/10 © Jalal Kawash 2009 Elementary Set Theory Peeking into Computer Science
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Reading Assignment Mandatory: Chapter 2 – Sections 2.4 and 2.5 22
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Sets set  is a collection of objects; we call these objects the  elements  of the set. Examples: Students in this class form (ie, are elements of) a set 33
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Representing Small Sets Small sets can be represented by listing its  members A = {paper, scissors, rock} All possible choices in the game B = {pawn, rook, knight, bishop, queen, king} All chess pieces 44
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Representing Big Sets May not be possible to list all members Some sets are infinite A = {x | x is a current student at UofC} All current students at UofC 55
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Properties of Sets Duplicates are not allowed (or do not count)  {paper, scissors, rock} is the same as {paper, scissors,  rock, rock}  We should not repeat elements Order of members is irrelevant {paper, scissors, rock} 66
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Multi-sets Duplication is allowed {Sara, Sam, Frank, Julie, Sam, Frank} 77
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Ordered Tuples We use curly brackets (braces) to represent sets {rock, paper} = {paper, rock} If order is important we use ordered tuples (rock, paper) ≠ (paper, rock) Maybe meaning ( choice of player 1 choice of player 2 ) General form of a tuple: (v1, v2, v3, … vn) 88
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Set Inclusion  B means that all members of A are also  members of B Read A is a subset (or equal to) of B Examples: {1,2}   {1,2,7} 99
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c © Jalal Kawash 2009 Peeking into Computer Science  10/11/10 Set Membership We write x  S to say that x is an element of the  set S Examples: 2  {1, 2, 3} $  {$, ¢, £, ¥, €,  } a   {a} 10
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c © Jalal Kawash 2009
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2-3-4- Graphs and Trees (part 1) - c ElementarySetTheory

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