12h - 12-2 Discrete Mathematics Operations on Sets Previous...

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Introduction Operations on Sets Discrete Mathematics Andrei Bulatov Discrete Mathematics – Operations on Sets 12-2 Previous Lecture Sets and elements Subsets, proper subsets, empty sets Universe Cardinality Power set Discrete Mathematics – Operations on Sets 12-3 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 12-4 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 | 5 y x=2y} {x | 5 y x=3y} = {x | 5 y x=6y} + + = Z Q Z Discrete Mathematics – Operations on Sets 12-5 Union The union of sets A and B, denoted by A B, is the set that contains those elements that are 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 12-6 Disjoint Sets and Principle of Inclusion-Exclusion Sets A and B are said to be disjoint if A B = . Sets {Mon,Tue,Wed,Thu,Fri} and {Sat,Sun} are disjoint. Principle of inclusion-exclusion.
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12h - 12-2 Discrete Mathematics Operations on Sets Previous...

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