Venn Diagrams in Logic: Examples and Definitions

Explore Venn diagrams in logic through examples illustrating sets, key definitions, theoretical and practical examples. Understand concepts such as intersection and union of sets using numbers 0 to 9.

• Venn diagrams
• Logic
• Sets
• Definitions
• Examples

benedetti_a Follow

Uploaded on Oct 09, 2024 | 0 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.

Presentation Transcript

1. Unit 10 Logic and Venn Diagrams Presentation 1 Venn Diagrams: Example Presentation 2 Venn Diagrams: Key Definitions Presentation 3 Venn Diagrams: Illustrating Sets Presentation 4 Venn Diagrams: Theoretical Example Presentation 5 Venn Diagram: Practical Example

2. Unit 10 Logic and Venn Diagrams Venn Diagram: Example

3. Using the numbers 0, 1, 2, , 9 illustrate the sets: and Solution: Use a Venn diagram

4. Using the numbers 0, 1, 2, , 9 illustrate the sets: and 4 A B 4 is in BOTH sides

5. Using the numbers 0, 1, 2, , 9 illustrate the sets: and 7 4 9 A B 7 and 9 are only in set A

6. Using the numbers 0, 1, 2, , 9 illustrate the sets: and 1 7 2 4 3 9 5 A B 1, 2, 3 and 5 are only in set B

7. Using the numbers 0, 1, 2, , 9 illustrate the sets: and 0 1 7 2 6 4 3 9 5 8 A B 0, 6 and 8 are not in A or B

8. You have finished viewing the presentation Venn Diagrams: Example Please choose an option Return to the Start Presentation 2 Venn Diagrams: Key Definitions Presentation 3 Venn Diagrams: Illustrating Sets Presentation 4 Venn Diagrams: Theoretical Example Presentation 5 Venn Diagram: Practical Example

9. Unit 10 Logic and Venn Diagrams Venn Diagram: Key Definitions

10. Intersection: Members of both set A and set B A B

11. Union: Members of set A or set B or both A B

12. Complementary: Members not in the set A A

13. Universal Set: All members U

14. Subset: All members of set A are in set B A B

15. Number of elements in a set: Empty set:

16. You have finished viewing the presentation Venn Diagrams: Key Definitions Please choose an option Return to the Start Presentation 1 Venn Diagrams: Example Presentation 3 Venn Diagrams: Illustrating Sets Presentation 4 Venn Diagrams: Theoretical Example Presentation 5 Venn Diagram: Practical Example

17. Unit 10 Logic and Venn Diagrams Venn Diagrams: Illustrating Sets

18. U A B

19. U A B

20. U A B

21. U A B

22. U A B

23. U A B

24. U A B

25. U A B

26. U A B

27. U A B

28. You have finished viewing the presentation Venn Diagrams: Illustrating Sets Please choose an option Return to the Start Presentation 1 Venn Diagrams: Example Presentation 2 Venn Diagrams: Key Definitions Presentation 4 Venn Diagrams: Theoretical Example Presentation 5 Venn Diagram: Practical Example

29. Unit 10 Logic and Venn Diagrams Venn Diagrams: Theoretical Example

30. What is the shaded region? U A B

31. What is the shaded region? U A B

32. What is the shaded region? U A B

33. What is the shaded region? U B A C B ( A C )

34. What is the shaded region? U B A C B )' C A (

35. What is the shaded region? U B A C (A C B' )

36. You have finished viewing the presentation Venn Diagrams: Theoretical Example Please choose an option Return to the Start Presentation 1 Venn Diagrams: Example Presentation 2 Venn Diagrams: Key Definitions Presentation 3 Venn Diagrams: Illustrating Sets Presentation 5 Venn Diagrams: Practical Example

37. Unit 10 Logic and Venn Diagrams Venn Diagram: Practical Example

38. U 9 1 14 3 4 13 15 6 2 5 10 7 12 8 11 A B U = {Natural Numbers less than 16} Describe set A and set B A = {Even Numbers} B = {Prime Numbers}

39. U A B 14 12 13 21 28 18 26 24 16 27 19 30 22 20 15 23 10 11 29 25 C 17 Describe Sets U, A, B and C U = {10,11,12,13,14,........29,30} A = {Even Numbers} B = {Multiples of 3} C = {Multiples of 5}

40. You have finished viewing the presentation Venn Diagrams: Practical Example Please choose an option Return to the Start Presentation 1 Venn Diagrams: Example Presentation 2 Venn Diagrams: Key Definitions Presentation 3 Venn Diagrams: Illustrating Sets Presentation 4 Venn Diagrams: Theoretical Example

41. Kerjakan dengan mengarsir 2 arah. Clue: Untuk U (Gabungan, Union) Setelah diarsir 2 arah, jawabannya adalah area yang terkena arsir single maupun arsir silang. Untuk n (Irisan, Intersection, Overlap) Setelah diarsir 2 arah, jawabannya adalah area yang terkena arsir silang. (A C B' ) B ( A C )

42. 37 X 3 = 111 37 X 6 = 222 ? X ? = 333 ? X ? = 444 ? X ? = 555 ? X ? = 666 ? X ? = 777 ? X ? = 888 ? X ? = 999 (1 x 9 ) + 2 = 11 (12 x 9 ) + 3 = 111 (? x 9) + ? = 1111 (? x 9 + ? = 11111

43. Source: M. Burghes, Logics and Venn Diagrams , Lecture Material of Discrete Mathematics, Plymouth: Plymouth University, 2008

44. Applying Venn & Its Logics onto Programming and Database

45. Venn and Its Logics in Handling Database A B C Wished Output (D) 1 11 1 1 2 12 2 2 3 13 3 3 4 14 4 4 5 15 5 5 11 16 6 6 12 17 11 13 18 12 14 19 13 15 20 14 21 21 15 22 22 21 23 23 22 24 24 23 25 25 24 25

46. Venn and Its Logics in Handling Database Seorang staf IT pada sebuah perusahaan pembuat mobil Gokar memperoleh data sbb: A B C Wished Output (F) 1 11 1 1 Bahwa jumlah Gokar yang dibuat semuanya adalah 30 unit, masing-masing diberi tanda dengan angka 1 s.d. 30. 2 12 2 2 3 13 3 3 4 14 4 4 Gokar Kategori A terdiri dari15 unit Gokar sebagaimana tercantum pada tabel. 5 15 5 5 11 16 6 6 Gokar Kategori B terdiri dari 15 unit Gokar sebagaimana tercantum pada tabel. 12 17 11 Gokar Kategori C terdiri dari 6 unit Gokar sebagaimana tercantum pada tabel. 13 18 12 14 19 13 Kepala bagian Marketing meminta bantuan staf IT tsb untuk memilah sedemikian rupa, yaitu akan ada 16 unit Gokar yang dikirim ke Balikpapan besok pagi. 15 20 14 21 21 15 22 22 21 Seandainya Anda adalah staf IT tersebut, gambarkan diagram Venn yg menggambarkan problem ini dan tulislah formula untuk memilah 16 unit Gokar yg akan dikirim ke Balikpapan! 23 23 22 24 24 23 25 25 24 25

47. Logics in Handling Number Patterns 1 + 3 + 5 + 7 + 9 = 5^2

48. Nilai Mhs Nama 29/9 Venn 6/10 Venn 13/10 Venn Logics 13/10 Tugas 27/10 Matriks 3/11 Matriks Total Poin Bonus Abraham 1+1 1+1+1 - 60 - - 5 Anatasha 1+1+1 - 1 100 - 1+1 6 Dipo 1 1 - 95 1+1+1 1+1 7 Okto 1+1 1+1 - 90 1+1 1+1 8 Rivaldy 1 1+1 70 1+1 1+1 7 Michelle 1 - 1 95 - - 2 Lanang 1 - - 90 1 - 2 Natalia 1 1 - 90 1+1 - 4 Raka - 1 - 70 1 1+1+1 5 Lingga - - - 70 1 1+1+1 4 Tirta - - - 0 - - 0

49. U A B

50. U A B