CSCE 235
Handout
8: Sets
February 10, 2003
Examples
of Sets
|
Names |
Definitions |
|
Natural numbers |
N = { 0, 1, 2, 3, 4, 5, …} |
|
All integers (positive, zero, negative) |
Z = { …, -3, -2, -1, 0, 1, 2, 3, 4, 5, …} |
|
Positive integers |
Z+ = { 1, 2, 3, 4, 5, …} |
|
Rational numbers |
Q = {m/n | |
|
Irrational numbers |
A number which cannot be written in the form m/n with both m and n integers |
|
Real numbers |
R, rational or not. |
|
Complex numbers |
C have the form a+bi
where a and b are real numbers and |
}
.
Note: Z+
N
Z
Q
R
Intervals
Notation
for some special subsets of R, called intervals. For 
with a < b,
we define
closed
open
half open
half open
Laws
of Algebra of Sets
|
Laws |
Representation |
|
Commutative Laws |
|
|
Associative Laws |
|
|
Distributive Laws |
|
|
Idempotent Laws |
|
|
Identity Laws |
|
|
Domination Laws |
|
|
Double Complementation |
|
|
Complement Laws |
|
|
DeMorgan Laws |
|
|
Absorption Laws |
|
