Sets

1. SetOperations

2. Definition of Sets
Sets refer to a well
defined collection
of distinct objects.

3. Basic Terms
• Universal set (U)
 refers to the larger set from which we
choose some elements to form new sets.
 Set of integers: =... , -3, -2, -1, 0, 1, 2, 3, ...

4. Basic Terms
• Null Set or Empty Set -  or  
 a set that contains no element.
• Unit Set
 a set that contains one element.
• Finite Set
a set that has countable number of
elements.
• Infinite Set
a set that has uncountable number of
elements.

5. Basic Terms
• Subset
- Set B is a subset of set A if every
of set B is in set A.
• Proper Subset  
- If set A has some elements that are
set B, then B is a proper subset of A.
• Improper Subset 
- If set A has all elements of set B and
has all elements of A, then B is an
subset of A.

6. OPERATIONS on
Sets
1. Complement
i.Absolute Complement (A' )
-The complement of set A is a set all
elements in U that does not belong
A.
ii. Relative Complement (AB) or (A-
B)
-The difference of sets A and B is a
elements in A that does not belong

7. OPERATIONS on
Sets
2. Union (  )
- The union of two sets A and B is a
containing all elements which
sets A or B.
3. Intersection (  )
- The intersection of two sets A and B
the set of all elements that belong to
the given sets.

8. Properties of Union
o Commutative  AB = B
A
o Identity  A = A
o Associative  A(BC) =
(AB)C

9. Properties of
Intersection
o Commutative  A  B = B 
A
o Identity  A  U= A
o Inverse  A  A'= 
o Associative  A(B C) =
(AB)C

10. Properties
o DPMA
1.A  (B C) = (AB)  (AC)
2. A  (BC) = (AB)  (AC)

11. Venn Diagram
o Picturing Sets (John Venn)
oVenn Diagram or Euler Circles

12. Given that A and B are the given sets
1. A B
either
or
2. A B
both
and
B
A
B
A
B
A

13. Given that A and B are the given sets
3. A'
Absolute
4. A - B
Relative
Complement
A
A'
B
A

14. Problems
1. Of 60 women interviewed, 24 used
creamsilk, 28 used sunsilk and 11 used both?
a. How many used either creamsilk or
sunsilk?41
b. neither creamsilk nor sunsilk. 19
c. creamsilk only 13
d. did not use creamsilk 36
e. did not use both? 49

15. S
U= 60
C S
11
13 17
19

16. Problems
2. In a class of 150 sixth graders, 60 have had
chiken pox, 50 have had measles and 40 had
mumps. Moreover, 30 have had both C and Me, 15
have had both C and Mu, 10 have had both Me and
Mu, 5 had all three.
a. How many have not had any of these diseases?
b. Me and Mu but have not had C?
c. Me or C but have not had Mu?
d. C only
e. One disease only
f. Had at least two
g. At most two

17. Given that A and B are the given sets
U=60 S
A
c
11 17
13
19

18. Solutions:
a. How many used either creamsilk or
sunsilk? 41
b. neither creamsilk nor sunsilk. 19
c. creamsilk only. 13
d. did not use creamsilk. 36
e. did not use both? 49