4. Operations on Sets
In arithmetic, we have operations such
as addition, subtraction, multiplication,
and division that enables us to combine
numbers.
In sets, we have:
1.
2.
8. Intersection of Sets
is the set of elements that
are both members of A and B.
Take a look at this example:
Therefore, when listing we list only the
common element/s.
9. Intersection of Sets
is the set of elements that
are both members of A and B.
Therefore, when listing we list only the
common element/s.
Take a look at this example:
A B A ∩ B
15. How Do We List Intersections?
E = { cheese, milk, butter, bread }
F = { milk, puto, cassava, bread }
U
E F= { milk, bread }
First Set (E)
Cap Second Set (F)
Equal Sign
Opening Brace
element/s
Closing Brace
Their common elements are and .
Then, we write:
16. What if this is the case?
Q = { 2, 4, 6, 8, 10, …}
R = { 1, 3, 5, 7, 9, … }
17. Q = { 2, 4, 6, 8, 10, …}
R = { 1, 3, 5, 7, 9, … }
Two sets whose intersection is the
or are said to be
disjoint.
are sets who have
.
What if this is the case?
28. Union of Sets
is the set of elements that
are members of A, or members of
B or members of both A and B.
To make it simpler, set elements
were being .
29. Union of Sets
Take a look at this example:
When we list the elements in the
, we
and
.
If an element is in both sides,
.
30. Union of Sets
When we list the elements in the
, we
and
.
If an element is in both sides,
.
Take a look at this example:
A B
A ∪ B
31. A B
A ∪ B
Take a look at this example:
Union of Sets
32. C D
C ∪ D
Another example but this
time..
Union of Sets
33. C D
C ∪ D
Another example but this
time..
Union of Sets
43. • It is constructed with a collection of
Venn Diagram
A B
44. • The circles are drawn inside a
that represents the .
Venn Diagram
U
A B
45. • It is used as a way of illustrating
between different
.
Venn Diagram
U
A B
46. Example:
Venn Diagram
U
A B
List down the elements of the following sets:
1. 𝐴 3. 𝐴 ∩ 𝐵 5. 𝑈
2. 𝐵 4. 𝐴 ∪ 𝐵
Jose
Andres
Maz
Emilio
Antonio
Apolinario
47. List down the elements of the following sets:
1. 𝐴 = { 𝐽𝑜𝑠𝑒, 𝐴𝑛𝑑𝑟𝑒𝑠, 𝑀𝑎𝑧 }
Example:
Venn Diagram
U
A B
Jose
Andres
Emilio
Antonio
Apolinario
Maz
48. Example:
Venn Diagram
U
A B
List down the elements of the following sets:
2. 𝐵 = { 𝑀𝑎𝑧 , 𝐸𝑚𝑖𝑙𝑖𝑜, 𝐴𝑛𝑡𝑜𝑛𝑖𝑜 }
Jose
Andres
Emilio
Antonio
Apolinario
Maz
49. Example:
Venn Diagram
U
A B
List down the elements of the following sets:
3. 𝐴 ∩ 𝐵 = { 𝑀𝑎𝑧 }
Jose
Andres
Emilio
Antonio
Apolinario
Maz
50. Example:
Venn Diagram
U
A B
List down the elements of the following sets:
4. 𝐴 ∪ 𝐵 = { 𝐽𝑜𝑠𝑒 , 𝐴𝑛𝑑𝑟𝑒𝑠 , 𝑀𝑎𝑧 , 𝐸𝑚𝑖𝑙𝑖𝑜 , 𝐴𝑛𝑡𝑜𝑛𝑖𝑜 }
Jose
Andres
Emilio
Antonio
Apolinario
Maz
51. Example:
Venn Diagram
U
A B
List down the elements of the following sets:
5. 𝑈 = { 𝐽𝑜𝑠𝑒 , 𝐴𝑛𝑑𝑟𝑒𝑠, 𝑀𝑎𝑧, 𝐸𝑚𝑖𝑙𝑖𝑜, 𝐴𝑛𝑡𝑜𝑛𝑖𝑜, 𝐴𝑝𝑜𝑙𝑖𝑛𝑎𝑟𝑖𝑜}
Jose
Andres
Emilio
Antonio
Apolinario
Maz
56. Venn Diagram
U
J K
List down the elements of the
following sets:
1. 𝐽 = {𝑎𝑝𝑝𝑙𝑒, 𝑚𝑒𝑙𝑜𝑛, 𝑢𝑏𝑒} apple
banana
chico
ube
melon
grapes
papaya
57. Venn Diagram
U
J K
List down the elements of the
following sets:
2. 𝐾 = { 𝑔𝑟𝑎𝑝𝑒𝑠, 𝑐ℎ𝑖𝑐𝑜, 𝑢𝑏𝑒 } apple
banana
chico
ube
melon
grapes
papaya
58. Venn Diagram
U
J K
List down the elements of the
following sets:
3. 𝐽 ∩ 𝐾 = { 𝑢𝑏𝑒 } apple
banana
chico
ube
melon
grapes
papaya
59. Venn Diagram
U
J K
List down the elements of the
following sets:
4. 𝐽 ∪ 𝐾
= { 𝑎𝑝𝑝𝑙𝑒, 𝑚𝑒𝑙𝑜𝑛, 𝑢𝑏𝑒,
𝑔𝑟𝑎𝑝𝑒𝑠, 𝑐ℎ𝑖𝑐𝑜}
apple
banana
chico
ube
melon
grapes
papaya
60. Venn Diagram
U
J K
List down the elements of the
following sets:
5. 𝑈
= { 𝑎𝑝𝑝𝑙𝑒, 𝑚𝑒𝑙𝑜𝑛, 𝑢𝑏𝑒,
𝑔𝑟𝑎𝑝𝑒𝑠, 𝑐ℎ𝑖𝑐𝑜,
𝑝𝑎𝑝𝑎𝑦𝑎, 𝑏𝑎𝑛𝑎𝑛𝑎 }
apple
banana
chico
ube
melon
grapes
papaya