Union, Intersection, complement and Difference of 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)’=