CS 70
Discrete Mathematics for CS
Fall 2006
Papadimitriou & Vazirani
Lecture 1
Introduction to Sets
A
set
is a well defined collection of objects considered as a whole. These objects are called
elements
or
members
of a set, and they can be anything, including numbers, letters, people, cities, and even other sets.
By convention, sets are usually denoted by capital letters and can be described or defined by listing its
elements and surrounding the list by curly braces. For example, we can describe the set
A
to be the set
whose members are the first five prime numbers, or we can explicitly write:
A
=
{
2, 3, 5, 7, 11
}
. If
x
is an
element of
A
, we write
x
∈
A
. Similarly, if
y
is not an element of
A
, then we write
y
negationslash∈
A
. Two sets
A
and
B
are said to be equal, written as
A
=
B
, if they have the same elements. The order and repetition of elements
do not matter, so
{
red, white, blue
}
=
{
blue, white, red
}
=
{
red, white, white, blue
}
. Sometimes, more
complicated sets can be defined by using a different notation. For example, the set of all rational numbers
denoted by
Q
can be written as:
{
a
b

a
,
b
are integers,
b
negationslash
=
0
}
. In English, this is read as “the set of all
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 Fall '08
 HAULLGREN
 2k, Vazirani

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