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
4
9
A
2
3
5
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
4
9
8
A
2
3
5
0, 6 and 8 are not in A or B
6
B
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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
Intersection: Members of both set A and set B
A
B
Union: Members of set A or set B or both
A
B
Complementary: Members not in the set
A
A’
Universal Set: All members
U
Subset: All members of set A are in set B
A
B
Number of elements in a set:
Empty set:
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Venn Diagrams: Example
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Venn Diagrams: Illustrating Sets
Presentation 4
Venn Diagrams: Theoretical Example
Presentation 5
Venn Diagram: Practical Example
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
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Venn Diagrams: Illustrating Sets
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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
A
B
What is the shaded region?
U
A
B
What is the shaded region?
U
A
B
What is the shaded region?
B
A
C
B( A C)
U
What is the shaded region?
B
A
C
( A  B  C )'
U
What is the shaded region?
B
A
C
(A  C  B' )
U
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Venn Diagrams: Theoretical
Example
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Venn Diagrams: Example
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Venn Diagrams: Illustrating Sets
Presentation 5
Venn Diagrams: Practical Example
Unit 10 – Logic and
Venn Diagrams
Venn Diagram: Practical Example
1
10
12
A
9
14
4
6
U
3
13
2
15
5
7
8
11
B
U = {Natural Numbers less than 16}
Describe set A and set B
A = {Even Numbers}
B = {Prime Numbers}
A
U
B
14
12
28
26
18
24
16
22
13
21
27
19
30
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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Example
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Presentation 4
Venn Diagrams: Theoretical Example
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
37
?
?
?
?
?
?
?
(1
(12
(?
(?
X
X
X
X
X
X
X
X
X
3
6
?
?
?
?
?
?
?
x9)
x9)
x 9)
x9
=
=
=
=
=
=
=
=
=
111
222
333
444
555
666
777
888
999
+2
+3
+?
+?
= 11
= 111
= 1111
= 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
A
B
C
Wished
Output (F)
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
Seorang staf IT pada sebuah perusahaan pembuat
mobil Gokar memperoleh data sbb:
 Bahwa jumlah Gokar yang dibuat semuanya adalah
30 unit, masing-masing diberi tanda dengan angka 1
s.d. 30.
 Gokar Kategori A terdiri dari15 unit Gokar
sebagaimana tercantum pada tabel.
 Gokar Kategori B terdiri dari 15 unit Gokar
sebagaimana tercantum pada tabel.
 Gokar Kategori C terdiri dari 6 unit Gokar
sebagaimana tercantum pada tabel.
 Kepala bagian Marketing meminta bantuan staf IT tsb
untuk memilah sedemikian rupa, yaitu akan ada 16
unit Gokar yang dikirim ke Balikpapan besok pagi.
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!
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