1
Section 6.1
Sets and Set Operations
A
set
is a collection of objects.
An
element
is an object of a set.
Notation:
∈
= “element of”
∉
= “not an element of”
Example: Let
A
be the set of all prime numbers. 2 is an element of
A
and 3 is an element
of
A
; but, 4 is not an element of
A
.
A
∈
2
,
A
∈
3
,
A
∉
4
The set C = {
x

4
2
=
x
} is in
set builder notation
.
The set C can also be written as follows:
C = {2, 2}.
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: Let
A
be the set of all prime numbers and
B
be the set of all integers. Then,
A
is
a subset of
B
.
B
A
⊆
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.