1 / 15

CSE 2353 – September 25 th 2002

CSE 2353 – September 25 th 2002. Relations. Set Partitions. Math Review. Hamming Distance Error Correction. Relations. A R B is a subset of A X B a  A is related to b  B iff (a,b)  R Example: A = B = {1,2,3,4,5,6}; R = {(a,b): a divides b}. Display of Relations. X-Y Plot

amos-myers
Download Presentation

CSE 2353 – September 25 th 2002

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSE 2353 – September 25th 2002 Relations

  2. Set Partitions

  3. Math Review

  4. Hamming DistanceError Correction

  5. Relations • A R B is a subset of A X B • a  A is related to b  B iff (a,b)  R • Example: • A = B = {1,2,3,4,5,6}; • R = {(a,b): a divides b}

  6. Display of Relations • X-Y Plot • Two Lines • Dia-graph • “Adjacency” Matrix

  7. Types of Relations • Identity • Universal • Inverse • n-Ary

  8. Properties of Relations • Reflexive (a R a) • Symmetric • Anti-Symmetric • Transitive

  9. Graphic Representation • Properties of the relation:

  10. Set Terms • R  S • R  S • R and S are Reflexive • R and S are Symmetric • R and S are anti-symmetric • R and S are Transitive

  11. Equivalence Relation • What Properties? • reflexive? • anti-symmetric? • symmetric? • transitive?

  12. Equivalence Classes • Congruence modulo n • a-b = kn

  13. Partial Ordering • a R b iff a <= b • a R b iff a < b

  14. Min and Max Elements

  15. Properties • Reflexive iff aRa for all aA • Symmetric iff aRb -> bRa for all a,bA • Anti-symmetric iff aRb and bRa -> a=b for all a,bA • Transitive iff aRb and bRc -> aRc • Example: R is a relation on the real numbers: xRy iff x  y

More Related