Demonstration Teaching

2. Mathematics
in the Modern world

6. Problem Solving

7. Problem Solving

8. Problem Solving

9. Set Theory

10. Set Theory

11. Set Theory

12. Set Theory
4,7,8,21
The symbol “ ∈ ” express
membership.
7 ∈ B
7 is an element of set B.

13. Set Theory
4,5,8,13
7 ∉ V
8 is an element of set V.
8 ∈ V

14. Set Theory
4,5,7,14
8 ∉ F
14 is an element of set F.
14 ∈ F

15. Set Theory

16. Set Theory

17. Set Theory

18. Methods of Describing Set

19. Methods of Describing Set

20. Methods of Describing Set

21. Methods of Describing Set

22. Methods of Describing Set
Jojo, Max, Cindy, Carla
m, i, s, e

23. Methods of Describing Set

24. Methods of Describing Set

25. Methods of Describing Set
 
A= Integers 1 6
x x
 

26. Some Special Sets
The Null Set or Empty Set. This is a set with
no elements, often symbolized by
or { }
The Universal Set. This is the set of all elements
currently under consideration, and is often
symbolized by
U


27. Universal Sets
The universal set is the set of all things pertinent to a
given discussion and is designated by the symbol U
Example:
U = {all students at AMAU}
Some Subsets:
A = {all Computer Technology students}
B = {freshmen students}
C = {sophomore students}

28. Universal Sets

29. Universal Sets
4,7,8,21
4,5,8,13
4,5,7,14
4,5,7,8,13,14,21

30. Universal Sets
4,7,8,21
4,5,8,13
4,5,7,14
4,5,7,8,13,14,21
The sets B, V, and F are
contained in the universal
set, then these sets are also
called subsets of the
Universal set.
 B ⊂ U (A is the subset of U)
 V ⊂ U (B is the subset of U)
 F ⊂ U (C is the subset of U)

31. Subsets and Superset
1,2,3,4
1,2,3
3,4,5

32. Subsets and Superset
1,2,3,4
1,2,3
3,4,5
7,8,9,10
9,10

33. Power Set
In set theory, the power set (or
power set) of a Set A is defined as the set of
all subsets of the Set A including the Set
itself and the null or empty set. It is
denoted by P(A). Basically, this set is the
combination of all subsets including null
set, of a given set.

34. Power Set
In set theory, the
power set (or power set) of
a Set A is defined as the set
of all subsets of the Set A
including the Set itself and
the null or empty set. It is
denoted by P(A). Basically,
this set is the combination
of all subsets including null
set, of a given set.
A = { a, b, c }
P(A) = { { } , { a }, { b },
{ c }, { a, b }, { b, c },
{ c, a }, { a, b, c } }
2𝑛
23
=8

35. Find the Subsets
What are all the subsets of C={3, 4, 5}
P(C)={} or Ø, {3}, {4}, {5} {3,4}, {3,5}, {4,5} {3,4,5}

36. Power Set
7,8,9,10 9,10

37. Joint and Disjoint Sets

38. Joint and Disjoint Sets
7,8,9,10 9,10
A∩B = 9,10
A and B are joint sets

39. Joint and Disjoint Sets
7,8,9,10 1,2,3
A∩B = ∅
A and B are disjoint sets

40. Joints and Disjoint Sets
B∩V∩F = 4
B∩V = 8
V∩F= 5

41. Diagrams show that set(s) are
subsets of the universal set (U)
4,7,8,21
M ⊂

42. Diagrams show that set(s) are
subsets of the universal set (U)

43. Diagrams show that set(s) are
subsets of the universal set (U)
Universal Set
Sets A & B

44. Diagrams show that set(s) are
subsets of the universal set (U)

45. Diagrams show that set(s) are
subsets of the universal set (U)

46. Diagrams show that set(s) are
subsets of the universal set (U)

47. Diagrams show that set(s) are
subsets of the universal set (U)

48. Set Complement
~A or A′
“A complement,” or “not A” is the set of all
elements not in A.
*What the others have that you don’t*

49. Practice:
U
black
purple A red
white blue green
Types of color
Universal set U =
What is the complement of set A?

50. More Practice:
U = {1, 2, 3, 4, 5} is the universal set and
A = {2, 3}. What is A′?
U = {a, b} is the universal set and
T = {a}. What is T′?
U = {+, -, x, ÷, =} is the universal set and
A = {÷, =}. What is A′?