Understanding 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.
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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
Unit 10 Logic and Venn Diagrams Venn Diagram: Example
Using the numbers 0, 1, 2, , 9 illustrate the sets: and Solution: Use a Venn diagram
Using the numbers 0, 1, 2, , 9 illustrate the sets: and 4 A B 4 is in BOTH sides
Using the numbers 0, 1, 2, , 9 illustrate the sets: and 7 4 9 A B 7 and 9 are only in set A
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
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
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
Unit 10 Logic and Venn Diagrams Venn Diagram: Key Definitions
Number of elements in a set: Empty set:
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Unit 10 Logic and Venn Diagrams Venn Diagrams: Illustrating Sets
U A B
U A B
U A B
U A B
U A B
U A B
U A B
U A B
U A B
U A B
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
Unit 10 Logic and Venn Diagrams Venn Diagrams: Theoretical Example
What is the shaded region? U B A C B ( A C )
What is the shaded region? U B A C B )' C A (
What is the shaded region? U B A C (A C B' )
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Unit 10 Logic and Venn Diagrams Venn Diagram: Practical Example
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}
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}
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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 )
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
Source: M. Burghes, Logics and Venn Diagrams , Lecture Material of Discrete Mathematics, Plymouth: Plymouth University, 2008
Applying Venn & Its Logics onto Programming and Database
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
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
Logics in Handling Number Patterns 1 + 3 + 5 + 7 + 9 = 5^2
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
U A B
U A B
