1. Relations

2. Binary Relations a relation between elements of two sets is a subset of their Cartesian product (of ordered pairs). Note the di ff erence 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

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