L06-1 - Relations (Graph View) Relations (on a set)...

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Re la tio ns
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Binary Relations a  re la tio n b e twe e n e le m e nts  o f two  s e ts  is  a  s ub s e t  o f the ir C a rte s ia n pro duc t (o f o rde re d pairs ).  No te  the  di e re nc e  b e twe e n a  re la tio n a nd a   f func tio n: in a  re la tio n, e ac h a    A c a n m a p to   m ultiple  e le m e nts  in B. Thus , re la tio ns  a re   g e ne ra liza tio ns  o f func tio ns .  If a n o rde re d pa ir (a , b )   R the n we  s a y tha t a  is   re la te d to  b . We  m a y a ls o  us e  the  no ta tio n a Rb . 
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Relations
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Unformatted text preview: Relations (Graph View) Relations (on a set) Reflexivity Symmetry I Symmetry II Symmetric Relations Transitivity Transitivity Combining Relations Composition and Powers Power Examples Equivalence Relations Equivalence Classes I Equivalence Classes II Partitions I Partitions II Matrix Interpretation Equivalence Relations (Example-I) Equivalence Relations (Example-II) Equivalence Relations (Example-III) Equivalence Relations (Example-IV) Partial Order I Partial Order II Equivalence Relations (Example-IV) Definition Comparability Total Orders Hasse Diagram Hasse Diagram Example...
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This note was uploaded on 04/22/2010 for the course CS 23022 taught by Professor Staff during the Spring '08 term at Kent State.

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L06-1 - Relations (Graph View) Relations (on a set)...

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