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ics141-lecture08-Functions

# ics141-lecture08-Functions - University of Hawaii ICS141...

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8-1 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii ICS141: Discrete Mathematics for Computer Science I Department of Information and Computer Sciences University of Hawaii Stephen Y. Itoga

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8-2 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii Lecture 8 Chapter 2. Basic Structures 2.2. Set Operations 2.3 Functions
8-3 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii Some 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. Baek

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8-4 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii Previously… Variable objects x , y , z ; sets S , T , U . Literal set {a, b, c} and set-builder notation { x | P ( 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 S × T. Set operators: , , - .
8-5 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii Generalized Union Binary union operator: A B n -ary union: A 1 A 2 A n = ((…(( A 1 A 2 ) …) A n ) (grouping & order is irrelevant) “Big U” notation: More generally, union of the sets A i for i I : For infinite number of sets: - I i i A n i i A 1 = = 1 i i A

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8-6 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii Generalized Intersection Binary intersection operator: A B n -ary intersection: A 1 A 2 A n ((…(( A 1 A 2 ) …) A n ) (grouping & order is irrelevant) “Big Arch” notation: More generally, intersection of the sets A i for i I : For infinite number of sets: n i i A 1 = I i i A = 1 i i A
8-7 ICS 141: Discrete Mathematics I (Spr 2008) University of Hawaii } 1 { } 3 , 2 , 1 { } 2 , 1 { } 1 { 3 2 1 1 = = = = A A A A i i

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ics141-lecture08-Functions - University of Hawaii ICS141...

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