The document discusses different types of relations including reflexive relations, symmetric relations, transitive relations, and equivalence relations. It provides definitions of each type of relation and includes examples of relations represented as directed graphs and matrices.

1. Reflexive Relation – (12 - 2)

2. Reflexive Relation – (12 – 2a)

3. Example – (12 - 3)

4. Example – (12 – 3a)

5. Example – (12 – 3b)

6. Directed Graph of a Reflexive Relation – (12 - 4)

7. Directed Graph of a Reflexive Relation – (12 – 4a)

8. Directed Graph of a Reflexive Relation – (12 - 5)

9. Directed Graph of a Reflexive Relation – (12 – 5)

10. Matrix Representation of a Reflexive Relation – (12 - 6)

11. Example – (12 – 6a)

12. Symmetric Relation – (12 - 7)

13. Example – (12 - 8)

14. Example – (12 – 8a)

15. Directed Graph of a Symmetric Relation – (12 - 9)

16. Example – (12 – 9a)

17. Example – (12 – 9b)

18. Example – (12 – 9c)

19. Example – (12 – 9d)

20. Matrix Representation of a Symmetric Relation – (12 - 11)

21. Example – (12 – 11a)

22. Example – (12 - 12)

23. Example – (12 – 12a)

24. Example – (12 - 13)

25. Example – (12 – 13a)

26. Directed Graph of a Transitive Relation – (12 - 14)

27. Example – (12 - 3)

28. Example – (12 – 14a)

29. Example – (12 – 15a)

30. Example – (12 – 15b)

31. Exercise – (12 - 19)

32. Exercise – (12 – 19a)

33. Solution – (12 – 19b)

34. Equivalence Relation – (12 - 32)

35. Example – (12 – 32a)