Open for improvements. Thanks God bless us all.

2. Basic
Ideas of
Sets
Part 3

3. Operations
on Sets

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.

5. Intersection
of Sets

6. Intersection of Sets
Read as..
The of sets A and B.

7. Intersection of Sets
The ∩ is a special math symbol called
.

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

10. Intersection of Sets
Take a look at this example:
A B A ∩ B

11. Intersection of Sets
Take a look at this example:
A B A ∩ B

12. Intersection of Sets
Let’s take another example:
C D C ∩ D

13. Intersection of Sets
Let’s take another example:
C D C ∩ D

14. Intersection of Sets
Let’s take another example:
C D C ∩ D

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?

18. More Intersections
S = { a, b, c, d, e, f }
T = { f, g, h, j, k, l, a }

19. More Intersections
S = { 1, 3, 5, 7, 9, … }
T = { 17 }
11, 13, 15,17, … }

20. Intersections now with
Complement

21. Intersections now with
Complement

22. Intersections now with
Complement

23. Intersections now with
Complement

25. Union of
Sets

26. Union of Sets
Read as..
The of Sets A and B.

27. Union of Sets
The symbol for union is the
, ∪.

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

34. More examples:
Union of Sets
A = { a, e, i, o, u }
B = { a, b, c, d, e }
A ∪ B =

35. More examples:
Union of Sets
U = { a, b, c, d, e }
A = {a, b, c }
B = { c, d, e }
A’ ∪ B’ =

36. Union of Sets
U = { 1, 2, 3, 4, 5 }
A = { 1, 3, 5 }
B = { 3, 4, 5 }
C = { 2, 4 }
A’ ∪ B’ =

37. Union of Sets
U = { 1, 2, 3, 4, 5 }
A = { 1, 3, 5 }
B = { 3, 4, 5 }
C = { 2, 4 }
(A ∪ B)’=

38. Union of Sets
U = { 1, 2, 3, 4, 5 }
A = { 1, 3, 5 }
B = { 3, 4, 5 }
C = { 2, 4 }
(A ∪ C)’ =

39. Examine:
Union of Sets
A = { 2, 4, 6, 8, … }
B = { 1, 3, 5, 7, … }
A ∪ B =

41. Venn
Diagram

42. • Introduced by in 1880.
Venn Diagram

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

53. TRY THIS!

54. Venn Diagram
U
J K
List down the elements of
the following sets:
1. 𝐽
2. 𝐾
3. 𝐽 ∩ K
4. 𝐽 ∪ 𝐾
5. 𝑈
apple
banana
chico
ube
melon
grapes
papaya

55. ANSWERS!

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