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ECS20 Handout 3
January 6, 2011
1. A
set
is an unordered colleciton of objects
Notation:
A, B, C, .
..
2. The objects in a set are also called the
elements
, or
members
, of the set. A set is said to contain
its elements.
3. Two sets
A
and
B
are
equal
if and only if they have the same elements.
A
=
B
↔ ∀
x
(
x
∈
A
↔
x
∈
B
).
4. The set
A
is said to be a
subset
of
B
iF every element of
A
is also an element of
B
.
A
⊆
B
↔ ∀
x
(
x
∈
A
→
x
∈
B
).
Proper subset:
A
⊂
B
if
∀
x
(
x
∈
A
→
x
∈
B
)
∧ ∃
x
(
x
∈
B
∨
x
n∈
A
).
5. ±or every set
S
, the empty (null) set Ø
∈
S
and
S
⊆
S
.
6. Universal set
U
contains all objectives under considerations.
7. Venn diagram
8. If there are
n
distinct elements in the set
S
where
n
is a nonnegative integer, we say that
S
is a
²nite set.
n
=

S

is the
cardinality
of
S
.
A set is said to be in²nite if it is not ²nite.
9. Given a set
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 Winter '08
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