This document defines and provides examples of set operations including: - Union of sets, which is the set of all elements that are in set A, B, or both. - Intersection of sets, which is the set of all elements common to both sets A and B. - Complement of a set, which is the set of all elements in the universal set that are not in the given set. - Difference of two sets, which is the set of elements in A that are not in B. It then provides exercises for the reader to practice identifying unions, intersections, complements, and differences of various sets.

1. Operations on
Set

2. Identify if each statement is true or false.
Given: U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
1. The universal set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
2. {2, 4, 6, 8, 10} is a subset of U.
3. {0, 10} is a subset of U.
4. Empty set { } is a subset of U.
5. The cardinality number of set U is 10.
True or False

3. Union of Sets
01
Intersection of Sets
02
Difference of Two Sets
03
Complement of a set
04
Table of contents

4. Union of Sets (Combination)
The union of sets A and B, written
as A 𝖴 B, is the set of elements that
are members of A, or members of B,
or members of both A and B.
01

5. 1. Given: A = {1, 2, 3} B = {1, 2, 4, 5, 6},
2. Given: A = {a, b, c, d, e} B = {a, e, i, o, u},
3. Given: A = {Monday, Tuesday, Wednesday, Thursday,
Friday} B = {Saturday, Sunday}
Examples

6. Exercises 1
1. Given:
C= {2, 4, 6, 8, 10} D= {2, 4, 6, 8} E= {2,
6, 8, 12}
F= {8, 10} G= {2, 3, 4} H= {2}
Find:
a. 𝐶 ∪ 𝐸
b. 𝐶 ∪ 𝐺
c. 𝐷 ∪ 𝐹
d. D ∪ 𝐻
e. 𝐸 ∪ 𝑁

7. Exercises 1
2. {multiples of 2 less than 15} ∪ {multiples of 2 greater than
15}
3. {letters in the word LOVE} ∪ {letter in the word MOVE}
4. {vowels} ∪ {consonants}

8. Intersection of Sets
(Common Element)
The intersection of two sets A and B,
written as A ∩ B, is the set of all elements
common to both sets A and B.
02

9. Exercises 2
1. Given:
C= {2, 4, 6, 8, 10} D= {2, 4, 6, 8} E= {2,
6, 8, 12}
F= {8, 10} G= {2, 3, 4} H= {2}
Find:
a. 𝐶 ∩ 𝐸
b. 𝐶 ∩ 𝐺
c. 𝐷 ∩ 𝐹
d. D ∩ 𝐻
e. 𝐸 ∩ 𝑁

10. Exercises 2
2. {multiples of 2 less than 15} ∩ {multiples of 2 greater than
15}
3. {letters in the word LOVE} ∩ {letter in the word MOVE}
4. {vowels} ∩ {consonants}

11. Complement of Set
The complement of a set A, written
as A’, is the set of all the elements in
the universal set (U) that are not in
set A.
03

12. Examples
Given:
U = {a, e, i, o, u} B = { a, e, u }
C = {i, o, u} D = { }
1. B’=
2. C’=
3. D’ =
4. U’=

13. Exercises 3
Given: U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C= {2, 4, 6, 8, 10} D= {1, 3, 5, 7, 9} E= {2, 6, 8, 12}
F= {8, 10} G= {2, 3, 4} H= { }
Find:
1. C’=
2. D’=
3. E’=
4. F’=
5. G’=
6. H’=

14. Difference of Two Sets
The difference of set A and B, written as A
– B, is a set of elements in A that are not
in B.
04

15. Examples
1. A = {1, 2, 3} and B = {1, 2, 4, 5, 6}
A – B =
B – A =
2. C = {a, b, c, d, e} and D = {a, e, i, o, u}
C – D =
D – C =

16. Exercises 4
Given:
C= {1, 4, 5, 8, 10} D= {1, 2, 5, 8, 9} E= {2, 6, 8, 12}
F= {8, 10} G= {2, 3, 4}
Find:
1. C – B =
2. E – D =
3. D – F =
4. G – C =
5. D – G =

17. Activity
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A= {1, 2, 3, 4, 5}
B= {1, 2, 4, 6, 8} C = {4, 5, 7, 9, 10}
Find
1. A’ =
2. B’ =
3. C’ =
4. A ∩ B=
5. A ∩ C=
6. B ∩ C=

18. 7. A U B=
8. B U C=
9. A U C=
10. A ∩ (BUC)=
11. A U (B ∩ C)=
12. A’ ∩ B’=
13. A U B’
14. A’ ∩ C=
15. (A U B)’=