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Chapter 1
(1.1 Sets)
p
()
September 2, 2009
Sets
• A set is a collection of objects,
order is not taken into account.
bjects = elements members
• Objects = elements, members
• How to describe it?
yl
ist
inga
l
lmembers: A={1234}
– By listing all members:
A = {1,2,3,4}
– By listing a property necessary for membership:
B = {x  x is a positive, even integer}
– Symbol:
jinah@cs.kaist.ac.kr
2
CS204 Discrete Math (Fall 2009)
Sets
•E
l
em
e
n
t
•
Cardinality
– If X is a finite set,
we let X = number of elements in X

• Example:
what is the cardinality of the set {R,Z} =?
•
embership
Membership
• Empty (or null or void) set,
• Two sets X and Y are equal: X=Y
– For every x, if
x
X, then
x
Y, and
for every x,
if
x
x
X.
•
ubset A
B
Subset
A
B
• Proper subset
A
B
• Power set: set of all subsets (proper or not) of a set X
(p p
)
– Formal proof in Section 2.4
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 Spring '08
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