1 / 32

Relations

Relations. Binary Relations. a relation between elements of two sets is a subset of their Cartesian product (of ordered pairs). Note the di fference between a relation and a function: in a relation, each a ∈ A can map to multiple elements in B. Thus, relations are generalizations of functions.

jack
Download Presentation

Relations

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. Relations

  2. Binary Relations • a relation between elements of two sets is a subset of their Cartesian product (of ordered pairs). • Note the difference between a relation and a function: in a relation, each a ∈ A can map to multiple elements in B. Thus, relations are generalizations of functions. • If an ordered pair (a, b) ∈ R then we say that a is related to b. We may also use the notation aRb.

  3. Relations

  4. Relations (Graph View)

  5. Relations (on a set)

  6. Reflexivity

  7. Symmetry I

  8. Symmetry II

  9. Symmetric Relations

  10. Transitivity

  11. Transitivity

  12. Combining Relations

  13. Composition and Powers

  14. Power Examples

  15. Equivalence Relations

  16. Equivalence Classes I

  17. Equivalence Classes II

  18. Partitions I

  19. Partitions II

  20. Matrix Interpretation

  21. Equivalence Relations (Example-I)

  22. Equivalence Relations (Example-II)

  23. Equivalence Relations (Example-III)

  24. Equivalence Relations (Example-IV)

  25. Partial Order I

  26. Partial Order II

  27. Equivalence Relations (Example-IV)

  28. Definition

  29. Comparability

  30. Total Orders

  31. Hasse Diagram

  32. Hasse Diagram Example

More Related