A set is an unordered collection of elements. Elements might be people, days of the week, colors, numbers, etc. We may indicate the elements of a set by listing them between brackets. The set of prime numbers less than 10 is expressed {2, 3, 5, 7}. Alternatively, we may use the notation {x: property} to indicate the set of all elements x satisfying the indicated property. In this manner, the same set of prime numbers less than 10 is expressed as {x: x < 10 and x is prime}. You should be familiar with the following sets:
We denote intervals of real numbers with parentheses or
braces, depending upon whether or not end points are included. The
interval (2, 3) is the set {x: 2 < x < 3}. The interval [5,
10) is the set {x: 5
If a is an element of A, we denote this a
A set B is a subset of
A if every element of B is an element of A. We
indicate this relationship with the notation B
Two sets are said to be disjoint
if their intersection is
If A
If A
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:
the 
:
the set of 
:
the set of 
:
the set of 
:
the set of 
.
x < 10}. 
A. We read this "a is contained in A." Otherwise, we
say "a is not contained in A" and indicate that relationship
with a
A.
A.
The empty set
D
that contains all elements that are either elements of C and/or
elements of D. The 
D
that contains all elements that are both elements of C and
elements of D. Generalizing to more than two sets, let
be
a collection of sets. We define their union as the set of elements that
belong to at least one of the sets
. We define
the intersection of the sets as the set of elements that belong to every
set 
,
which is pronounced "the complement of A" or "A complement."
has neither a maximum nor a minimum. We can generalize the notion of
maximum and minimum with the notions of 
