Section 6.1 – Sets and Set Operations
1
Section 6.1
Sets and Set Operations
A collection of objects is called a
set.
An object of a set is called an
element.
Notation:
∈
= “element of”
∉
= “not an element of”
The set C = {
x

9
2
=
x
} is in
set builder notation
.
The set C can also be written as follows:
C = {3, 3}.
Let
A
and
B
be two sets.
If every element of
A
is also in
B
,
A
is said to be a
subset
of
B
.
Notation:
⊆
= “subset of”
⊆
/
= “not a subset of”
Example 1:
Let C = {1,2,3,4,5,6}, D = {2,4,6}, E = {2,1,6,4,3,5}, and G = {1, 4, 6}.
Which of the following is/are true?
I.
D
⊆
C
II.
E
⊆
/
C
III.
D
⊆
G
The set
A
is a
proper subset
of a set
B
(Notation:
B
A
⊂
) if the following two
conditions hold.
1.
B
A
⊆
2.
There exists at least one element in
B
that is not in
A
.
Example 2:
Let G = {5,6,7,8,9,10}, H = {5,8,10}, I = {8, 5}, and J = {5,8}. Which of the
following is/are true?
I.
H
⊂
G
II.
H
⊂
J
III.
J
⊂
H
IV.
I
⊄
J