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Unformatted text preview: Introduction Operations on Sets Discrete Mathematics Discrete Mathematics – Operations on Sets 122 Previous Lecture Sets and elements Subsets, proper subsets, empty sets Universe Cardinality Power set MIDTERM When: Wednesday, October 6, regular time 10:30 Where: Here Topics covered:  Propositional logic  Predicates and quantifiers  Sets and set operations All lectures needed for the midterm are already posted. Discrete Mathematics – Operations on Sets 124 Venn Diagrams Often it is convenient to visualize various relations between sets. We use Venn diagrams for that. universe set A B B is a subset of A Discrete Mathematics – Operations on Sets 125 Intersection The intersection of sets A and B, denoted by A ∩ B, is the set that contains those elements in both A and B. A ∩ B = { x  x ∈ A ∧ x ∈ B} A B A ∩ B Examples {1,3,5,7} ∩ {2,3,4,5,6} = {3,5} {Jan.,Feb.,Dec.} ∩ {Jan.,Feb.,Mar.} = {Jan.,Feb.} {x  ∃ y x=2y} ∩ {x  ∃ y x=3y} = {x  ∃ y x=6y} Discrete Mathematics – Operations on Sets 126 Union The union of sets A and B, denoted by A ∪ B, is the set that contains those elements that are either in A or in B. A B Examples A ∪ B = { x  x ∈ A ∨ x ∈ B} A ∪ B {Mon,Tue,Wed,Thu,Fri} ∪ {Sat,Sun} = {Mon,Tue,Wed,Thu,Fri,Sat,Sun} {1,3,5,7} ∪ {2,3,4,5,6} = {1,2,3,4,5,6,7} Discrete Mathematics – Operations on Sets 127 Disjoint Sets and Principle of InclusionExclusion Sets A and B are said to be disjoint...
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This note was uploaded on 12/12/2010 for the course MACM 201 taught by Professor Marnimishna during the Fall '09 term at Simon Fraser.
 Fall '09
 MarniMishna

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