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Unformatted text preview: 81ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiICS141: Discrete Mathematics for Computer Science IDepartment of Information and Computer SciencesUniversity of HawaiiStephen Y. Itoga82ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiLecture 8Chapter 2. Basic Structures2.2. Set Operations2.3 Functions83ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiSome material in these slides were taken/adapted from the slides made by Prof. Michael P. Frank and Prof. Jonathan L. Gross which are provided through the publisher of Discrete Mathematics and Its Applications written by Kenneth H. Rosen.Some slides are from Prof. Baek84ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiPreviouslyVariable objects x, y, z; sets S, T, U.Literal set {a, b, c} and setbuilder notation {xP(x)}.relational operator, and the empty set .Set relations =, , , , , , etc.Venn diagrams.Cardinality S and infinite sets N, Z, R.Power sets P(S).Cartesian product ST.Set operators: , , .85ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiGeneralized UnionBinary union operator: ABnary union:A1A2An= ((((A1A2))An)(grouping & order is irrelevant)Big U notation:More generally, union of the sets Aifor i I:For infinite number of sets:IiiAniiA1==1iiA86ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiGeneralized IntersectionBinary intersection operator: ABnary intersection:A1A2An((((A1A2))An)(grouping & order is irrelevant)Big Arch notation:More generally, intersection of the sets Aifor i I:For infinite number of sets:niiA1=IiiA=1iiA87ICS 141: Discrete Mathematics I (Spr 2008)University of Hawaii}1{}3,2,1{}2,1{}1{3211====AAAAiiGeneralized Intersection ExamplesLet Ai= {i, i+1, i+2,}. Then,Let Ai= {1, 2, 3,,i } for i= 1, 2, 3,. Then,,...}2,1,{,...}2,1,{,...}4,3,2{,...}3,2,1{3211++=++===nnnnnnAAAAAnnii88...
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This note was uploaded on 09/12/2008 for the course ICS 141 taught by Professor Idk during the Fall '08 term at Hawaii.
 Fall '08
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