12a-Operations-on-Sets

12a-Operations-on-Sets - Introduction Operations on Sets...

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Unformatted text preview: Introduction Operations on Sets Discrete Mathematics Discrete Mathematics – Operations on Sets 12-2 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 12-4 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 12-5 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 12-6 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 12-7 Disjoint Sets and Principle of Inclusion-Exclusion 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.

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12a-Operations-on-Sets - Introduction Operations on Sets...

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