1.
2.
3.
4.
Sets and Elements
Union and Intersection
Subset and Empty Set
Universal Set and Complement
1
A
set is any collection of objects. The objects,
which may be countries, cities, years, numbers,
letters, or anything else, are called the elements of
the set. A set is often specified by a listing of its
elements inside a pair of braces. A set may also be
specified by giving a description of its elements.
2
1.
The set of the first six letters of the alphabet is
{a, b, c, d, e, f}.
2.
{2, 4, 6, 8, 10} is the set
{the even numbers between 1 and 11}.
3.
The graph {(a,b) where b = a2} is a set with
infinitely many elements.
3
Let
A = {years
from 1991 to 2004
in which
unemployment is
at least 6%}.
Let B = {years
from 1991 to 2004
in which inflation
is at least 3%}.
4
Using
the table, the two sets are
A = {1991, 1992, 1993, 1994, 2003} and
B = {1991, 1992, 1993, 1996, 2000}.
5
The
union of A and B, denoted A B, is the set
consisting of all those elements that belong to
either A or B or both. The intersection of A and B,
denoted A B, is the set consisting of those
elements that belong to both A and B.
6
Let
A = {1991, 1992, 1993, 1994, 2003} and
B = {1991, 1992, 1993, 1996, 2000} from the
previous example. Find
A B = {1991,1992,1993,1994,1996,2000,2003}
A
B = {1991,1992,1993}
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A
set B is called a subset of A provided that every
element of B is also an element of A.
The set that contains no elements at all is the
empty set (or null set) and is written as. The empty
set is a subset of every set.
8
List
all possible subsets of {a, b, c}.

{a},
{b}, and {c}
{a,
b}, {a, c}, and {b, c}
{a,
b, c}
9
The
set U that contains all the elements of the sets
being discussed is called a universal set (for the
particular problem).
If A is a subset of U, the set of elements in U that
are not in A is called the complement of A, denoted
by A'.
10
Let
U = {a,b,c,d,e,f,g}, S = {a,b,c} and T =
{a,c,d}.
Find
S  = {d,e,f,g}
T  = {b,e,f,g}

S

T

 = {b,d,e,f,g}
11
A set is a collection of objects. Each object is
called an element of the set. The empty set is the set
containing no objects.
 The union of two sets is the set consisting of all
elements that belong to at least one of the sets. The
intersection of two sets is the set consisting of all
elements that belong to both of the sets.

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Set A is a subset of set B if every element of set A
is also an element of set B. In each situation or
problem, all sets are considered to be subsets of a
universal set. The set of all elements in the universal
set that do not belong to the set A is called the
complement of A, denoted A'.

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