Sets and Logic
Chapter 1
(1.1 Sets)
September 2, 2009
Sets
•
A set is a collection of objects,
d
i
t t k
i t
t
order is not taken into account.
Objects = elements members
•
Objects = elements, members
•
How to describe it?
By listing all members: A = {1 2 3 4}
– 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:
[email protected]
2
CS204 Discrete Math (Fall 2009)
Sets
•
Element
C
•
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} =?
•
Membership
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
Y, then
x
X.
•
Subset
A
B
Subset
A
•
Proper subset
A
B
•
Power set: set of all subsets (proper or not) of a set X
[email protected]
3
CS204 Discrete Math (Fall 2009)
Sets
•
Power set
If X


2
n
•
If X = n, 
 = 2
– Formal proof in Section 2.4
•
Set operations
– Union
Union
– Intersection
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Unkown
 Set Theory, Basic concepts in set theory

Click to edit the document details