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Lecture 12

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Discrete Mathematics

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Lecture 12

1. 1. Functions – (15 - 2)
2. 2. Functions – (15 – 2a)
3. 3. Example – (15 - 3)
4. 4. Solution – (15 – 3a)
5. 5. Solution – (15 – 3b)
6. 6. Solution – (15 – 3c)
7. 7. Function – (15 - 5)
8. 8. Remarks – (15 – 5a)
9. 9. Arrow Diagram of a Function – (15 - 6)
10. 10. Example – (15 – 6a)
11. 11. Example – (15 – 6b)
12. 12. Nonfunction – (15 - 7)
13. 13. Range of a Function – (15 - 8)
14. 14. Remarks – (15 – 8a)
15. 15. Exercise – (15 - 9)
16. 16. Exercise – (15 – 9a)
17. 17. Solution – (15 – 9b)
18. 18. Graph of a Function – (11 - 11)
19. 19. Graph of a Function – (15 – 11a)
20. 20. Graph of a Function – (15 – 11b)
21. 21. Vertical Line Test – (15 - 12)
22. 22. Example – (15 - 13)
23. 23. Solution – (15 – 13a)
24. 24. Solution – (15 – 13b)
25. 25. Exercise – (15 - 15)
26. 26. Exercise – (15 – 15a)
27. 27. Exercise – (15 – 15b)
28. 28. Exercise – (15 - 17)
29. 29. Exercise – (15 – 17a)
30. 30. Exercise – (15 – 17b)
31. 31. Exercise – (15 - 18)
32. 32. Solution – (15 – 18a)
33. 33. Functions Not Well Defined – (15 - 20)
34. 34. Solution – (15 – 20a)
35. 35. Solution – (15 – 20b)
36. 36. Exercise – (15 - 21)
37. 37. Solution – (15 – 21a)
38. 38. Solution – (15 - 22)
39. 39. Binary Operations – (15 - 28)
40. 40. Example – (15 – 28a)