FOR: Math 104 - Logic and Set Theory NOTE: I included my motivation before the topic is introduced. Let the students identify the elements, symbols, or notation in every station based on their previous knowledge. There are exercises, and the answers are provided in the last part. Thank you!

2. START

3. or { }
STATION 1

4. 
STATION 2

5. n(A)
STATION 3

6. 
STATION 4

7. {x l P(x)}
STATION 5

8. A~B
STATION 6

9. U
STATION 7

10. A'or A
STATION 8

11. A B
STATION 9

12. (a,b)
STATION 10

13. 
STATION 11

14. AxB
STATION 12

15. A B
STATION 13

16. P(S)
STATION 14

17. STATION 15


18. INTRODUCTION TO
SET THEORY
Prepared by:
S herwin V. Labadan BS E D-2

19. S E T THE OR Y
19
is a branch of mathematics that
studies sets or the mathematical
science of the inifite.
It studies properties of sets and
help people to organize things into
groups.

20. 1 C orinthians
14:40
20
"B ut all things must be
done properly and in
order."

21. GEORG CANTOR
(1848-1918)
21

22. 22
is any well-defined collection of
“objects.”
are the objects in the set.
of the sets

23. A = {a, b, c, d, e, f,...}
Sets elements
E xamples of
S ets:
BS E D-Math female= {Welcez, R onah, Julie,
R oxanne, C harmaine}C olors ofa rainbow= {red, orange, yellow, green, blue,
indigo, violet}
S tate ofmatter={solid, liquid, gas, plasma}
A={x lx is a positive integer less
than 10}
B={x lx is a setofvowel letters}

24. B={x lx is a setofvowel
letters}
B={a, e, i, o,
u}
a
B
 b B
an object is an
element of a set
an object is NOT
an element of a set

25. ME THODS OF
WR ITING S E TS
25
“Tabulation
Method”
“Set Builder
Notation”
-the elements of
the sets are
enumerated
-a descriptive
phrase
{x l P(x)}
B={a,e,i,o,u} B={x lx is a setofvowel lette
E xampl
e:
E xampl
e:

26. A={x lx is a positive integer
less than 10}
A={1,2,3,4,5,6,7,8,9}
C ={xlx is a letter in the word dirtC ={d, i, r, t}
D={xlx is odd and x>2}D={3,5,7,9,11,... }

27. }F INITE S E TS
setwhose
elements are
limited or
countable

28. }
INF INITE
S E TSsetwhose
elements are
unlimited or
uncountable

29. UNIT
SET
setwith one one
element“Singleton”
E MP T Y
S E T“”Null Set”
or { }
setwith no
elements
setofall elements currently
under considerationUNIVE R S AL
S E T U or 
------------
--------------
--------

30. EXERCISE 1
1. P={xl x is a whole number greater than 1 but
less than 3}2. M={xl x is an integer less than 2 butgreater
than 1}3. S ={xl x is the setofpositive integers less
than zero}
 4. U={3,6,9,12,15,18,21,24,27}
5. Q={Xia}
6. L={xl x is a vowel letter ofthe word
rhythm }

31. C AR DINALITY
31
T he cardinalnumber of a set is the
number or elements or members
in the set
n(A)

32. The cardinal
number of A is 9 or
n (A)= 9.
{1,2,3,4,5,6,7,8,9}
T he cardinal
number of C is 4
or n (C )= 4.
T he cardinal
number of B is 5 or
n (B )= 5.

33. EXERCISE 2
1. 
2. Q={1,2,3}
3. I={ }
4. V= {{1,2,3},{4,5}}
5. H={ ,{a},{b}, {a,b}}

34. VENN
DIAGRAM“Set Diagram”
- a picturial presentation
ofrelation and
operations on sets
JOHN VENN
(1834-1923)

35. S UBS E T
35
IfA and B are sets, A is called
subsetofB
A B
ifand only if, every elementofA is
also an elementofB.
BxAxxBA  ,

36. A
B
U
a
b
cd
e
f
g
A={c,d,e}
U={a,b,c,d,e,f,g}
B={a,b,c,d,e}
A B

37. PR OPE R
S UBS E T
37
IfA and B are sets, A is a proper
subsetofB
ifand only if, every elementofA is in B,
butthere is atleastone elementofB
thatis notin A.
A B

38. A
B
U
a
b
cd
e
f
g
A={c,d,e}
U={a,b,c,d,e,f,g}
B={a,b,c,d,e}
C
C ={a,b,c,d,e}
BA
CA
BA
BC 

39. E QUAL S E T
39
G iven setA and B, A equals B
ifand only if, every elementofA is in B,
and every elementofB is in A.
BA
ABBABA 

40. A
B
U
a
b
cd
e
f
g
A={c,d,e}
U={a,b,c,d,e,f,g}
B={a,b,c,d,e}
C
C ={a,b,c,d,e}
CB 
BC 
CB 

41. POWE R S E T
41
G iven a setS from universe U, the
power setofS
is the collection (or sets) ofall subsets
ofS .
)(SP
2
n

42. 1. A= {e, f} as it is a
subset of all
sets
2. S ={0, 1, 2}
}}2,1,0{},2,1{},2,0{},1,0{},2{},1{},0{,{)( SP
}},{},{},{,{)( fefeAP 
2)( An 4)( AP
3)( Sn 8)( SP
}{)(.3 P
0)( n 1)( P

43. SET OPERATIONS
43

44. UNION
44
The union ofA and B,
is the setofall elements ofx in U
such thatx is in A or x is in B.
}{ BxAxlxBA 
BA

45. INTE R S E C TIO
N
45
The intersection ofA and B,
is the setofall elements ofx in U
such thatx is in A and x is in B.
}{ BxAxlxBA 
BA

46. DIS JOINT S E TS
46
 BA
Two sets are called disjoint(or non-
intersecting) ifand only if, they have no
elements in common

47. C OMPLE ME NT
47
The complementofA (or absolute
complementofA)
is the setofall elements ofx in U
such thatx is notin A
}{' AUlxxA 
'A

48. DIF F E R E NC E
48
The diffference ofA and B
(or relative complementofA and B)
is the setofall elements ofx in U
such thatx is in A and x is notin B.
'{~ BABxAxlxBA 
BA~

49. S YMME TR IC
DIF F E R E NC E
49
their symmetric difference as the set
containing ofall elements thatbelong to A or
to B, butnotto both and B
)}()({ BAxBAxlxBA 
BA
IfsetA and B are two sets
)(~)()'()( BABAorBABAor 

50. OR DE R E D PAIR
50
In the ordered pair,
),( ba
a is called the firstcomponentand
b is the second component
),(),( abba 

51. EXERCISE 3
1. (2,5)=(9-7,
2+3)
2. {2,5} ≠ {5,2}
3. (2,5) ≠ (5,2)
TR UE OR
F ALS E

52. C AR TE S IAN
PR ODUC T
52
The C artesian productofsets A and B,
AxB
}),{( BAandblabaAxB 
is

53. F ind the cartesian productofa
given set:
A={2,3,5} and B={7,8}
1. AxB=
{(2,7),(2,8),(3,7),(3,8),(5,7),(5,8)}
2. BxA={(7,2),(8,2),(7,3),(8,3),(7,5),(8,5)}
3. AxA=
{(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)}
EXAMPLE

54. Identify the elements of a given
kind of set and its cardinality
1. A= {xlx is a consonant letter
of
s upercalifragilis ticexpialidoci
ous }
2. B = {xlx is a squares of the
first five counting number}
3. S et C contains all the
factors of 244. D= {xlx is an positive integer, -
QUIZ

55. L et U= {postive integers from
1 to 10}
A= {1,2,4,6,8,10}
B = {1,3,5,7,8,9}
C = {1,2,3}
D= {2,3,4}
E = {3,4,5}
F = {4,5,6}
F IND:
1.
2.
3.
4.
5.
'' BA
FED 
EC
DB
EA

56. ANSWER KEY
S tation 1: Null S et
S tation 2: Proper
S ubset
S tation 3:
C ardinality
S tation 4: S ubset
S tation 5: R ule
Method
S tation 6:
Difference
S tation 7:
Universal S et
S tation 8:
C omplement
S tation 9:
S tation 11: E lement
S tation 12: C artesian
Product
S tation 13: Union
S tation 14: Power S et
S tation 15: Universal S et
E XE R C IS E 1:
1. Unitset
2. E mpty set
3. E mpty set
4. Universal set
5. Unitset
6. E mpty set

57. E XE R C IS E 2:
1. 0
2. n( Q)=3
3. n(I)=1
4. n(V)=2
5. n(H)=4
E XE R C IS E 3:
1. TR UE
2. F ALS E
3. TR UE
QUIZ:
1. A={s,u,p,e,r,c,a,l,i,f,g,t,x,d,o,u}
n(A)=16
2. B={1,4,9,16,25}
n(B)=5
3. C ={1, 2, 3, 4, 6, 8, 12, 24}
n(C )=8
4. D={1,2,3,4,5,6,7,8,9}
n(D)=9
1. {2,3,4,5,6,7,8,9,10}
2. {4}
3. {1,2,4,5}
4. {1,5,7,8,9}
5. {1,2,3,4,5,6,8, 10}

58. Thank you
for sliding!
@ S ecretC LS he
rwin
S herwin Barcelona Villa
Labadan
slabadan8@ gmail.com
+F ollow me
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